Edit Profile (opens in new tab) Cranston, Daniel W. Compute Distance To: Compute 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 all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 1143.05025Cranston, Daniel W. 41 2006 Regular bipartite graphs are antimagic. Zbl 1210.05141Cranston, Daniel W. 33 2009 Regular graphs of odd degree are antimagic. Zbl 1321.05229Cranston, Daniel W.; Liang, Yu-Chang; Zhu, Xuding 22 2015 Injective colorings of graphs with low average degree. Zbl 1218.05046Cranston, Daniel W.; Kim, Seog-Jin; Yu, Gexin 22 2011 Injective colorings of sparse graphs. Zbl 1209.05075Cranston, Daniel W.; Kim, Seog-Jin; Yu, Gexin 22 2010 List-coloring the square of a subcubic graph. Zbl 1172.05023Cranston, Daniel W.; Kim, Seog-Jin 21 2008 Pebbling and optimal pebbling in graphs. Zbl 1142.05046Bunde, David P.; Chambers, Erin W.; Cranston, Daniel; Milans, Kevin; West, Douglas B. 18 2008 Star coloring of sparse graphs. Zbl 1179.05042Bu, Yuehua; Cranston, Daniel W.; Montassier, Mickaël; Raspaud, André; Wang, Weifan 17 2009 An introduction to the discharging method via graph coloring. Zbl 1355.05104Cranston, Daniel W.; West, Douglas B. 17 2017 Game matching number of graphs. Zbl 1286.05133Cranston, Daniel W.; Kinnersley, William B.; O, Suil; West, Douglas B. 13 2013 A new lower bound on the density of vertex identifying codes for the infinite hexagonal grid. Zbl 1186.05070Cranston, Daniel W.; Yu, Gexin 12 2009 Linear choosability of sparse graphs. Zbl 1225.05095Cranston, Daniel W.; Yu, Gexin 9 2011 Coloring claw-free graphs with \(\Delta-1\) colors. Zbl 1268.05069Cranston, Daniel W.; Rabern, Landon 8 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 1329.39018Cranston, Daniel W.; Kent, Candace M. 6 2013 Brooks’ theorem and beyond. Zbl 1330.05061Cranston, Daniel W.; Rabern, Landon 6 2015 Graphs with \(\chi=\Delta\) have big cliques. Zbl 1321.05080Cranston, Daniel W.; Rabern, Landon 6 2015 Planar graphs of girth at least five are square \((\delta + 2)\)-choosable. Zbl 1402.05043Bonamy, Marthe; Cranston, Daniel W.; Postle, Luke 6 2019 The \(1,2,3\)-conjecture and \(1,2\)-conjecture for sparse graphs. Zbl 1303.05172Cranston, Daniel W.; Jahanbekam, Sogol; West, Douglas B. 5 2014 Short proofs for cut-and-paste sorting of permutations. Zbl 1128.05001Cranston, Daniel W.; Sudborough, I. Hal; West, Douglas B. 5 2007 Coloring a graph with \(\Delta-1\) colors: conjectures equivalent to the Borodin-Kostochka conjecture that appear weaker. Zbl 1303.05032Cranston, Daniel W.; Rabern, Landon 4 2015 Edge-choosability and total-choosability of planar graphs with no adjacent 3-cycles. Zbl 1198.05044Cranston, Daniel W. 4 2009 Crossings, colorings, and cliques. Zbl 1182.05035Albertson, Michael O.; Cranston, Daniel W.; Fox, Jacob 4 2009 A note on coloring vertex-transitive graphs. Zbl 1310.05087Cranston, Daniel W.; Rabern, Landon 4 2015 Revolutionaries and spies on trees and unicyclic graphs. Zbl 1262.05024Cranston, Daniel W.; Smyth, Clifford D.; West, Douglas B. 4 2012 Planar graphs have independence ratio at least 3/13. Zbl 1344.05051Cranston, Daniel W.; Rabern, Landon 4 2016 Sufficient sparseness conditions for \(G^2\) to be \((\Delta + 1)\)-choosable, when \(\Delta \geq 5\). Zbl 1300.05093Cranston, Daniel W.; Škrekovski, Riste 4 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 1162.05020He, Wenjie; Zhang, Lingmin; Cranston, Daniel W.; Shen, Yufa; Zheng, Guoping 3 2008 List-coloring the squares of planar graphs without 4-cycles and 5-cycles. Zbl 1368.05047Cranston, Daniel W.; Jaeger, Bobby 3 2017 Revolutionaries and spies: spy-good and spy-bad graphs. Zbl 1257.05096Butterfield, Jane V.; Cranston, Daniel W.; Puleo, Gregory J.; West, Douglas B.; Zamani, Reza 3 2012 Choosability of the square of a planar graph with maximum degree four. Zbl 1296.05053Cranston, Daniel W.; Erman, Rok; Škrekovski, Riste 3 2014 Painting squares in \(\Delta^2-1\) shades. Zbl 1339.05124Cranston, Daniel W.; Rabern, Landon 2 2016 Subcubic edge-chromatic critical graphs have many edges. Zbl 1370.05062Cranston, Daniel W.; Rabern, Landon 2 2017 New results in \(t\)-tone coloring of graphs. Zbl 1266.05009Cranston, Daniel; Kim, Jaehoon; Kinnersley, William 2 2013 List colorings of \(K_5\)-minor-free graphs with special list assignments. Zbl 1248.05062Cranston, Daniel W.; Pruchnewski, Anja; Tuza, Zsolt; Voigt, Margit 2 2012 Modified linear programming and class 0 bounds for graph pebbling. Zbl 1384.90112Cranston, Daniel W.; Postle, Luke; Xue, Chenxiao; Yerger, Carl 2 2017 Edge lower bounds for list critical graphs, via discharging. Zbl 1424.05081Cranston, Daniel W.; Rabern, Landon 1 2018 Sparse graphs are near-bipartite. Zbl 1450.05025Cranston, Daniel W.; Yancey, Matthew P. 1 2020 The fractional chromatic number of the plane. Zbl 1399.05069Cranston, Daniel W.; Rabern, Landon 1 2017 Planar graphs are \(9/2\)-colorable. Zbl 1397.05061Cranston, Daniel W.; Rabern, Landon 1 2018 Vertex partitions into an independent set and a forest with each component small. Zbl 1470.05131Cranston, Daniel W.; Yancey, Matthew P. 1 2021 Vertex partitions into an independent set and a forest with each component small. Zbl 1470.05131Cranston, Daniel W.; Yancey, Matthew P. 1 2021 Sparse graphs are near-bipartite. Zbl 1450.05025Cranston, Daniel W.; Yancey, Matthew P. 1 2020 Planar graphs of girth at least five are square \((\delta + 2)\)-choosable. Zbl 1402.05043Bonamy, Marthe; Cranston, Daniel W.; Postle, Luke 6 2019 Edge lower bounds for list critical graphs, via discharging. Zbl 1424.05081Cranston, Daniel W.; Rabern, Landon 1 2018 Planar graphs are \(9/2\)-colorable. Zbl 1397.05061Cranston, Daniel W.; Rabern, Landon 1 2018 An introduction to the discharging method via graph coloring. Zbl 1355.05104Cranston, Daniel W.; West, Douglas B. 17 2017 List-coloring the squares of planar graphs without 4-cycles and 5-cycles. Zbl 1368.05047Cranston, Daniel W.; Jaeger, Bobby 3 2017 Subcubic edge-chromatic critical graphs have many edges. Zbl 1370.05062Cranston, Daniel W.; Rabern, Landon 2 2017 Modified linear programming and class 0 bounds for graph pebbling. Zbl 1384.90112Cranston, Daniel W.; Postle, Luke; Xue, Chenxiao; Yerger, Carl 2 2017 The fractional chromatic number of the plane. Zbl 1399.05069Cranston, Daniel W.; Rabern, Landon 1 2017 Planar graphs have independence ratio at least 3/13. Zbl 1344.05051Cranston, Daniel W.; Rabern, Landon 4 2016 Painting squares in \(\Delta^2-1\) shades. Zbl 1339.05124Cranston, Daniel W.; Rabern, Landon 2 2016 Regular graphs of odd degree are antimagic. Zbl 1321.05229Cranston, Daniel W.; Liang, Yu-Chang; Zhu, Xuding 22 2015 Brooks’ theorem and beyond. Zbl 1330.05061Cranston, Daniel W.; Rabern, Landon 6 2015 Graphs with \(\chi=\Delta\) have big cliques. Zbl 1321.05080Cranston, Daniel W.; Rabern, Landon 6 2015 Coloring a graph with \(\Delta-1\) colors: conjectures equivalent to the Borodin-Kostochka conjecture that appear weaker. Zbl 1303.05032Cranston, Daniel W.; Rabern, Landon 4 2015 A note on coloring vertex-transitive graphs. Zbl 1310.05087Cranston, Daniel W.; Rabern, Landon 4 2015 The \(1,2,3\)-conjecture and \(1,2\)-conjecture for sparse graphs. Zbl 1303.05172Cranston, Daniel W.; Jahanbekam, Sogol; West, Douglas B. 5 2014 Sufficient sparseness conditions for \(G^2\) to be \((\Delta + 1)\)-choosable, when \(\Delta \geq 5\). Zbl 1300.05093Cranston, Daniel W.; Škrekovski, Riste 4 2014 Choosability of the square of a planar graph with maximum degree four. Zbl 1296.05053Cranston, Daniel W.; Erman, Rok; Škrekovski, Riste 3 2014 Game matching number of graphs. Zbl 1286.05133Cranston, Daniel W.; Kinnersley, William B.; O, Suil; West, Douglas B. 13 2013 Coloring claw-free graphs with \(\Delta-1\) colors. Zbl 1268.05069Cranston, Daniel W.; Rabern, Landon 8 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 1329.39018Cranston, Daniel W.; Kent, Candace M. 6 2013 New results in \(t\)-tone coloring of graphs. Zbl 1266.05009Cranston, Daniel; Kim, Jaehoon; Kinnersley, William 2 2013 Revolutionaries and spies on trees and unicyclic graphs. Zbl 1262.05024Cranston, Daniel W.; Smyth, Clifford D.; West, Douglas B. 4 2012 Revolutionaries and spies: spy-good and spy-bad graphs. Zbl 1257.05096Butterfield, Jane V.; Cranston, Daniel W.; Puleo, Gregory J.; West, Douglas B.; Zamani, Reza 3 2012 List colorings of \(K_5\)-minor-free graphs with special list assignments. Zbl 1248.05062Cranston, Daniel W.; Pruchnewski, Anja; Tuza, Zsolt; Voigt, Margit 2 2012 Injective colorings of graphs with low average degree. Zbl 1218.05046Cranston, Daniel W.; Kim, Seog-Jin; Yu, Gexin 22 2011 Linear choosability of sparse graphs. Zbl 1225.05095Cranston, Daniel W.; Yu, Gexin 9 2011 Injective colorings of sparse graphs. Zbl 1209.05075Cranston, Daniel W.; Kim, Seog-Jin; Yu, Gexin 22 2010 Regular bipartite graphs are antimagic. Zbl 1210.05141Cranston, Daniel W. 33 2009 Star coloring of sparse graphs. Zbl 1179.05042Bu, Yuehua; Cranston, Daniel W.; Montassier, Mickaël; Raspaud, André; Wang, Weifan 17 2009 A new lower bound on the density of vertex identifying codes for the infinite hexagonal grid. Zbl 1186.05070Cranston, Daniel W.; Yu, Gexin 12 2009 Edge-choosability and total-choosability of planar graphs with no adjacent 3-cycles. Zbl 1198.05044Cranston, Daniel W. 4 2009 Crossings, colorings, and cliques. Zbl 1182.05035Albertson, Michael O.; Cranston, Daniel W.; Fox, Jacob 4 2009 List-coloring the square of a subcubic graph. Zbl 1172.05023Cranston, Daniel W.; Kim, Seog-Jin 21 2008 Pebbling and optimal pebbling in graphs. Zbl 1142.05046Bunde, David P.; Chambers, Erin W.; Cranston, Daniel; Milans, Kevin; West, Douglas B. 18 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 1162.05020He, Wenjie; Zhang, Lingmin; Cranston, Daniel W.; Shen, Yufa; Zheng, Guoping 3 2008 Short proofs for cut-and-paste sorting of permutations. Zbl 1128.05001Cranston, Daniel W.; Sudborough, I. Hal; West, Douglas B. 5 2007 Strong edge-coloring of graphs with maximum degree 4 using 22 colors. Zbl 1143.05025Cranston, Daniel W. 41 2006 all cited Publications top 5 cited Publications all top 5 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 all top 5 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 all top 5 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) Citations by Year