## Cranston, Daniel W.

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 Author ID: cranston.daniel-w Published as: Cranston, Daniel W.; Cranston, Daniel Homepage: http://www.people.vcu.edu/~dcranston/ External Links: MGP · ORCID · arXiv · dblp
 Documents Indexed: 57 Publications since 2006 Co-Authors: 49 Co-Authors with 49 Joint Publications 1,522 Co-Co-Authors
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### Co-Authors

 8 single-authored 15 Rabern, Landon 10 West, Douglas Brent 4 Yu, Gexin 3 Kim, Seog-Jin 3 Kinnersley, William B. 3 Milans, Kevin G. 2 O, Suil 2 Postle, Luke 2 Puleo, Gregory John 2 Škrekovski, Riste 2 Yancey, Matthew P. 1 Albertson, Michael O. 1 Bonamy, Marthe 1 Bu, Yuehua 1 Bunde, David P. 1 Bushaw, Neal 1 Butterfield, Jane V. 1 Chambers, Erin Wolf 1 Choi, Ilkyoo 1 Erman, Rok 1 Fox, Jacob 1 He, Wenjie 1 Jaeger, Bobby 1 Jahanbekam, Sogol 1 Kent, Candace M. 1 Kim, Jaehoon 1 Korula, Nitish 1 LeSaulnier, Timothy D. 1 Li, Jiaao 1 Liang, Yu-Chang 1 Montassier, Mickaël 1 Mullins, Charles 1 Pierron, Théo 1 Pruchnewski, Anja 1 Raspaud, André 1 Shen, Yufa 1 Smyth, Clifford 1 Stocker, Christopher J. 1 Sudborough, Ivan Hal 1 Tuza, Zsolt 1 Vandenbussche, Jennifer 1 Voigt, Margit 1 Wang, Wei-Fan 1 Xue, Chenxiao 1 Yerger, Carl R. 1 Zamani, Reza 1 Zhang, Lingmin 1 Zheng, Guoping 1 Zhu, Xuding
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### Serials

 11 Journal of Graph Theory 10 SIAM Journal on Discrete Mathematics 8 The Electronic Journal of Combinatorics 7 Discrete Mathematics 3 Combinatorica 2 Discrete Applied Mathematics 2 Journal of Combinatorial Theory. Series B 2 The Australasian Journal of Combinatorics 2 Discussiones Mathematicae. Graph Theory 2 Journal of Combinatorics 1 Information Processing Letters 1 Applied Mathematics and Computation 1 Theoretical Computer Science 1 European Journal of Combinatorics 1 Graphs and Combinatorics 1 Algorithmica 1 Journal of Combinatorial Optimization
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### Fields

 54 Combinatorics (05-XX) 3 Operations research, mathematical programming (90-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Difference and functional equations (39-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mathematics education (97-XX)

### Citations contained in zbMATH Open

40 Publications have been cited 344 times in 276 Documents Cited by Year
Strong edge-coloring of graphs with maximum degree 4 using 22 colors. Zbl 1143.05025
Cranston, Daniel W.
2006
Regular bipartite graphs are antimagic. Zbl 1210.05141
Cranston, Daniel W.
2009
Regular graphs of odd degree are antimagic. Zbl 1321.05229
Cranston, Daniel W.; Liang, Yu-Chang; Zhu, Xuding
2015
Injective colorings of graphs with low average degree. Zbl 1218.05046
Cranston, Daniel W.; Kim, Seog-Jin; Yu, Gexin
2011
Injective colorings of sparse graphs. Zbl 1209.05075
Cranston, Daniel W.; Kim, Seog-Jin; Yu, Gexin
2010
List-coloring the square of a subcubic graph. Zbl 1172.05023
Cranston, Daniel W.; Kim, Seog-Jin
2008
Pebbling and optimal pebbling in graphs. Zbl 1142.05046
Bunde, David P.; Chambers, Erin W.; Cranston, Daniel; Milans, Kevin; West, Douglas B.
2008
Star coloring of sparse graphs. Zbl 1179.05042
Bu, Yuehua; Cranston, Daniel W.; Montassier, Mickaël; Raspaud, André; Wang, Weifan
2009
An introduction to the discharging method via graph coloring. Zbl 1355.05104
Cranston, Daniel W.; West, Douglas B.
2017
Game matching number of graphs. Zbl 1286.05133
Cranston, Daniel W.; Kinnersley, William B.; O, Suil; West, Douglas B.
2013
A new lower bound on the density of vertex identifying codes for the infinite hexagonal grid. Zbl 1186.05070
Cranston, Daniel W.; Yu, Gexin
2009
Linear choosability of sparse graphs. Zbl 1225.05095
Cranston, Daniel W.; Yu, Gexin
2011
Coloring claw-free graphs with $$\Delta-1$$ colors. Zbl 1268.05069
Cranston, Daniel W.; Rabern, Landon
2013
On the boundedness of positive solutions of the reciprocal MAX-type difference equation $$x_n=\max\left\{\frac{A_{n-1}^1}{x_{n-1}},\frac{A_{n-1}^2}{x_{n-2}},\cdots,\frac{A_{n-1}^t}{x_{n-t}}\right\}$$ with periodic parameters. Zbl 1329.39018
Cranston, Daniel W.; Kent, Candace M.
2013
Brooks’ theorem and beyond. Zbl 1330.05061
Cranston, Daniel W.; Rabern, Landon
2015
Graphs with $$\chi=\Delta$$ have big cliques. Zbl 1321.05080
Cranston, Daniel W.; Rabern, Landon
2015
Planar graphs of girth at least five are square $$(\delta + 2)$$-choosable. Zbl 1402.05043
Bonamy, Marthe; Cranston, Daniel W.; Postle, Luke
2019
The $$1,2,3$$-conjecture and $$1,2$$-conjecture for sparse graphs. Zbl 1303.05172
Cranston, Daniel W.; Jahanbekam, Sogol; West, Douglas B.
2014
Short proofs for cut-and-paste sorting of permutations. Zbl 1128.05001
Cranston, Daniel W.; Sudborough, I. Hal; West, Douglas B.
2007
Coloring a graph with $$\Delta-1$$ colors: conjectures equivalent to the Borodin-Kostochka conjecture that appear weaker. Zbl 1303.05032
Cranston, Daniel W.; Rabern, Landon
2015
Edge-choosability and total-choosability of planar graphs with no adjacent 3-cycles. Zbl 1198.05044
Cranston, Daniel W.
2009
Crossings, colorings, and cliques. Zbl 1182.05035
Albertson, Michael O.; Cranston, Daniel W.; Fox, Jacob
2009
A note on coloring vertex-transitive graphs. Zbl 1310.05087
Cranston, Daniel W.; Rabern, Landon
2015
Revolutionaries and spies on trees and unicyclic graphs. Zbl 1262.05024
Cranston, Daniel W.; Smyth, Clifford D.; West, Douglas B.
2012
Planar graphs have independence ratio at least 3/13. Zbl 1344.05051
Cranston, Daniel W.; Rabern, Landon
2016
Sufficient sparseness conditions for $$G^2$$ to be $$(\Delta + 1)$$-choosable, when $$\Delta \geq 5$$. Zbl 1300.05093
Cranston, Daniel W.; Škrekovski, Riste
2014
Choice number of complete multipartite graphs $$K_{3*3,2*(k - 5),1*2}$$ and $$K_{4,3*2,2*(k - 6),1*3}$$. Zbl 1162.05020
He, Wenjie; Zhang, Lingmin; Cranston, Daniel W.; Shen, Yufa; Zheng, Guoping
2008
List-coloring the squares of planar graphs without 4-cycles and 5-cycles. Zbl 1368.05047
Cranston, Daniel W.; Jaeger, Bobby
2017
Revolutionaries and spies: spy-good and spy-bad graphs. Zbl 1257.05096
Butterfield, Jane V.; Cranston, Daniel W.; Puleo, Gregory J.; West, Douglas B.; Zamani, Reza
2012
Choosability of the square of a planar graph with maximum degree four. Zbl 1296.05053
Cranston, Daniel W.; Erman, Rok; Škrekovski, Riste
2014
Painting squares in $$\Delta^2-1$$ shades. Zbl 1339.05124
Cranston, Daniel W.; Rabern, Landon
2016
Subcubic edge-chromatic critical graphs have many edges. Zbl 1370.05062
Cranston, Daniel W.; Rabern, Landon
2017
New results in $$t$$-tone coloring of graphs. Zbl 1266.05009
Cranston, Daniel; Kim, Jaehoon; Kinnersley, William
2013
List colorings of $$K_5$$-minor-free graphs with special list assignments. Zbl 1248.05062
Cranston, Daniel W.; Pruchnewski, Anja; Tuza, Zsolt; Voigt, Margit
2012
Modified linear programming and class 0 bounds for graph pebbling. Zbl 1384.90112
Cranston, Daniel W.; Postle, Luke; Xue, Chenxiao; Yerger, Carl
2017
Edge lower bounds for list critical graphs, via discharging. Zbl 1424.05081
Cranston, Daniel W.; Rabern, Landon
2018
Sparse graphs are near-bipartite. Zbl 1450.05025
Cranston, Daniel W.; Yancey, Matthew P.
2020
The fractional chromatic number of the plane. Zbl 1399.05069
Cranston, Daniel W.; Rabern, Landon
2017
Planar graphs are $$9/2$$-colorable. Zbl 1397.05061
Cranston, Daniel W.; Rabern, Landon
2018
Vertex partitions into an independent set and a forest with each component small. Zbl 1470.05131
Cranston, Daniel W.; Yancey, Matthew P.
2021
Vertex partitions into an independent set and a forest with each component small. Zbl 1470.05131
Cranston, Daniel W.; Yancey, Matthew P.
2021
Sparse graphs are near-bipartite. Zbl 1450.05025
Cranston, Daniel W.; Yancey, Matthew P.
2020
Planar graphs of girth at least five are square $$(\delta + 2)$$-choosable. Zbl 1402.05043
Bonamy, Marthe; Cranston, Daniel W.; Postle, Luke
2019
Edge lower bounds for list critical graphs, via discharging. Zbl 1424.05081
Cranston, Daniel W.; Rabern, Landon
2018
Planar graphs are $$9/2$$-colorable. Zbl 1397.05061
Cranston, Daniel W.; Rabern, Landon
2018
An introduction to the discharging method via graph coloring. Zbl 1355.05104
Cranston, Daniel W.; West, Douglas B.
2017
List-coloring the squares of planar graphs without 4-cycles and 5-cycles. Zbl 1368.05047
Cranston, Daniel W.; Jaeger, Bobby
2017
Subcubic edge-chromatic critical graphs have many edges. Zbl 1370.05062
Cranston, Daniel W.; Rabern, Landon
2017
Modified linear programming and class 0 bounds for graph pebbling. Zbl 1384.90112
Cranston, Daniel W.; Postle, Luke; Xue, Chenxiao; Yerger, Carl
2017
The fractional chromatic number of the plane. Zbl 1399.05069
Cranston, Daniel W.; Rabern, Landon
2017
Planar graphs have independence ratio at least 3/13. Zbl 1344.05051
Cranston, Daniel W.; Rabern, Landon
2016
Painting squares in $$\Delta^2-1$$ shades. Zbl 1339.05124
Cranston, Daniel W.; Rabern, Landon
2016
Regular graphs of odd degree are antimagic. Zbl 1321.05229
Cranston, Daniel W.; Liang, Yu-Chang; Zhu, Xuding
2015
Brooks’ theorem and beyond. Zbl 1330.05061
Cranston, Daniel W.; Rabern, Landon
2015
Graphs with $$\chi=\Delta$$ have big cliques. Zbl 1321.05080
Cranston, Daniel W.; Rabern, Landon
2015
Coloring a graph with $$\Delta-1$$ colors: conjectures equivalent to the Borodin-Kostochka conjecture that appear weaker. Zbl 1303.05032
Cranston, Daniel W.; Rabern, Landon
2015
A note on coloring vertex-transitive graphs. Zbl 1310.05087
Cranston, Daniel W.; Rabern, Landon
2015
The $$1,2,3$$-conjecture and $$1,2$$-conjecture for sparse graphs. Zbl 1303.05172
Cranston, Daniel W.; Jahanbekam, Sogol; West, Douglas B.
2014
Sufficient sparseness conditions for $$G^2$$ to be $$(\Delta + 1)$$-choosable, when $$\Delta \geq 5$$. Zbl 1300.05093
Cranston, Daniel W.; Škrekovski, Riste
2014
Choosability of the square of a planar graph with maximum degree four. Zbl 1296.05053
Cranston, Daniel W.; Erman, Rok; Škrekovski, Riste
2014
Game matching number of graphs. Zbl 1286.05133
Cranston, Daniel W.; Kinnersley, William B.; O, Suil; West, Douglas B.
2013
Coloring claw-free graphs with $$\Delta-1$$ colors. Zbl 1268.05069
Cranston, Daniel W.; Rabern, Landon
2013
On the boundedness of positive solutions of the reciprocal MAX-type difference equation $$x_n=\max\left\{\frac{A_{n-1}^1}{x_{n-1}},\frac{A_{n-1}^2}{x_{n-2}},\cdots,\frac{A_{n-1}^t}{x_{n-t}}\right\}$$ with periodic parameters. Zbl 1329.39018
Cranston, Daniel W.; Kent, Candace M.
2013
New results in $$t$$-tone coloring of graphs. Zbl 1266.05009
Cranston, Daniel; Kim, Jaehoon; Kinnersley, William
2013
Revolutionaries and spies on trees and unicyclic graphs. Zbl 1262.05024
Cranston, Daniel W.; Smyth, Clifford D.; West, Douglas B.
2012
Revolutionaries and spies: spy-good and spy-bad graphs. Zbl 1257.05096
Butterfield, Jane V.; Cranston, Daniel W.; Puleo, Gregory J.; West, Douglas B.; Zamani, Reza
2012
List colorings of $$K_5$$-minor-free graphs with special list assignments. Zbl 1248.05062
Cranston, Daniel W.; Pruchnewski, Anja; Tuza, Zsolt; Voigt, Margit
2012
Injective colorings of graphs with low average degree. Zbl 1218.05046
Cranston, Daniel W.; Kim, Seog-Jin; Yu, Gexin
2011
Linear choosability of sparse graphs. Zbl 1225.05095
Cranston, Daniel W.; Yu, Gexin
2011
Injective colorings of sparse graphs. Zbl 1209.05075
Cranston, Daniel W.; Kim, Seog-Jin; Yu, Gexin
2010
Regular bipartite graphs are antimagic. Zbl 1210.05141
Cranston, Daniel W.
2009
Star coloring of sparse graphs. Zbl 1179.05042
Bu, Yuehua; Cranston, Daniel W.; Montassier, Mickaël; Raspaud, André; Wang, Weifan
2009
A new lower bound on the density of vertex identifying codes for the infinite hexagonal grid. Zbl 1186.05070
Cranston, Daniel W.; Yu, Gexin
2009
Edge-choosability and total-choosability of planar graphs with no adjacent 3-cycles. Zbl 1198.05044
Cranston, Daniel W.
2009
Crossings, colorings, and cliques. Zbl 1182.05035
Albertson, Michael O.; Cranston, Daniel W.; Fox, Jacob
2009
List-coloring the square of a subcubic graph. Zbl 1172.05023
Cranston, Daniel W.; Kim, Seog-Jin
2008
Pebbling and optimal pebbling in graphs. Zbl 1142.05046
Bunde, David P.; Chambers, Erin W.; Cranston, Daniel; Milans, Kevin; West, Douglas B.
2008
Choice number of complete multipartite graphs $$K_{3*3,2*(k - 5),1*2}$$ and $$K_{4,3*2,2*(k - 6),1*3}$$. Zbl 1162.05020
He, Wenjie; Zhang, Lingmin; Cranston, Daniel W.; Shen, Yufa; Zheng, Guoping
2008
Short proofs for cut-and-paste sorting of permutations. Zbl 1128.05001
Cranston, Daniel W.; Sudborough, I. Hal; West, Douglas B.
2007
Strong edge-coloring of graphs with maximum degree 4 using 22 colors. Zbl 1143.05025
Cranston, Daniel W.
2006
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### Cited by 474 Authors

 17 Cranston, Daniel W. 14 Bu, Yuehua 10 Rabern, Landon 10 Yu, Gexin 9 Zhu, Xuding 7 Havet, Frédéric 7 Katona, Gyula Y. 7 Raspaud, André 6 Xu, Baogang 6 Yang, Donglei 5 Borodin, Oleg Veniaminovich 5 Dong, Wei 5 Henning, Michael Anthony 5 Ivanova, Anna Olegovna 5 Lin, Wensong 5 Miller, Mirka 5 Papp, László F. 5 Phanalasy, Oudone 5 Zamora, José 4 Brandt, Axel 4 Chang, Gerard Jennhwa 4 Chen, Min 4 Choi, Ilkyoo 4 Dȩbski, Michał 4 Hurlbert, Glenn H. 4 Kim, Seog-Jin 4 Liang, Yu-Chang 4 Matamala, Martín 4 Tuza, Zsolt 4 Wang, Wei-Fan 4 West, Douglas Brent 4 Yu, Xiaowei 4 Zhu, Junlei 3 Bujtás, Csilla 3 Chang, Yulin 3 Dantas, Rennan 3 Dvořák, Zdeněk 3 Ferrara, Michael J. 3 Győri, Ervin 3 Hefetz, Dan 3 Hu, Jie 3 Jahanbekam, Sogol 3 Joos, Felix Claudius 3 Kinnersley, William B. 3 Li, Rui 3 Lidický, Bernard 3 Lu, Kai 3 Montassier, Mickaël 3 Ryan, Joe 3 Sampaio, Rudini Menezes 3 Sieben, Nándor 3 Śleszyńska-Nowak, Małgorzata 3 Song, Zixia 3 Stiebitz, Michael 3 Stolee, Derrick 3 Sun, Taixiang 3 Valicov, Petru 3 Vizer, Máté 3 Wang, Guanghui 3 Wu, Jian-Liang 3 Yancey, Matthew P. 3 Yue, Jun 2 Alfaro Montúfar, Carlos Alejandro 2 Arroyo, Alan 2 Bekmetjev, Airat 2 Bensmail, Julien 2 Berikkyzy, Zhanar 2 Bonamy, Marthe 2 Bruhn, Henning 2 Chang, Feihuang 2 Chen, Ming 2 Chitturi, Bhadrachalam 2 Cohen, Nathann 2 Cusack, Charles A. 2 Deng, Kecai 2 Derňár, Marek 2 Goddard, Wayne Dean 2 Hao, Rongxia 2 Haynes, Teresa W. 2 Hocquard, Hervé 2 Horn, Paul S. 2 Jin, Ligang 2 Junosza-Szaniawski, Konstanty 2 Kang, Yingli 2 Kincaid, Rex K. 2 Kostochka, Aleksandr Vasil’evich 2 Kumbhat, Mohit 2 Levit, Vadim E. 2 Li, Deming 2 Li, Wei-Tian 2 Li, Xiangwen 2 Lih, Kowei 2 Liu, Daphne Der-Fen 2 Loeb, Sarah J. 2 Lozano, Antoni 2 Lv, Jianbo 2 Mandrescu, Eugen 2 Messerschmidt, Kacy 2 Mohar, Bojan 2 Mora, Mercè ...and 374 more Authors
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### Cited in 54 Serials

 44 Discrete Applied Mathematics 44 Discrete Mathematics 19 The Electronic Journal of Combinatorics 18 Graphs and Combinatorics 15 Journal of Graph Theory 12 SIAM Journal on Discrete Mathematics 11 European Journal of Combinatorics 11 Journal of Combinatorial Optimization 10 Discrete Mathematics, Algorithms and Applications 8 Applied Mathematics and Computation 8 Discussiones Mathematicae. Graph Theory 5 Information Processing Letters 5 Theoretical Computer Science 4 Acta Mathematica Sinica. English Series 2 Journal of Combinatorial Theory. Series B 2 Journal of Computer and System Sciences 2 Acta Mathematicae Applicatae Sinica. English Series 2 Algorithmica 2 The Australasian Journal of Combinatorics 2 Combinatorics, Probability and Computing 2 Sibirskie Èlektronnye Matematicheskie Izvestiya 2 Mathematics in Computer Science 1 Houston Journal of Mathematics 1 Periodica Mathematica Hungarica 1 Canadian Mathematical Bulletin 1 International Journal of Mathematics and Mathematical Sciences 1 SIAM Journal on Computing 1 Siberian Mathematical Journal 1 Combinatorica 1 Journal of Symbolic Computation 1 Discrete & Computational Geometry 1 Applied Mathematics Letters 1 Journal of Global Optimization 1 Distributed Computing 1 Journal of Difference Equations and Applications 1 Séminaire Lotharingien de Combinatoire 1 Discrete Mathematics and Theoretical Computer Science. DMTCS 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Journal of Applied Mathematics and Computing 1 Central European Journal of Mathematics 1 Journal of Discrete Algorithms 1 Mediterranean Journal of Mathematics 1 Advances in Difference Equations 1 AKCE International Journal of Graphs and Combinatorics 1 Proyecciones 1 Advances in Mathematics of Communications 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Analysis and Mathematical Physics 1 Dynamic Games and Applications 1 Journal of the Operations Research Society of China 1 Journal of Mathematics 1 Communications in Combinatorics and Optimization 1 Prikladnaya Diskretnaya Matematika
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### Cited in 14 Fields

 261 Combinatorics (05-XX) 23 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 19 Computer science (68-XX) 8 Operations research, mathematical programming (90-XX) 5 Difference and functional equations (39-XX) 4 Information and communication theory, circuits (94-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Numerical analysis (65-XX)