Cao, Yan; Chen, Guantao On the average degree of edge chromatic critical graphs. (English) Zbl 07305048 J. Comb. Theory, Ser. B 147, 299-338 (2021). MSC: 05C15 PDF BibTeX XML Cite \textit{Y. Cao} and \textit{G. Chen}, J. Comb. Theory, Ser. B 147, 299--338 (2021; Zbl 07305048) Full Text: DOI
Brešar, Boštjan; Henning, Michael A. A \(\frac{3}{4}\)-approximation of Vizing’s conjecture for claw-free graphs. (English) Zbl 1443.05138 Discrete Appl. Math. 284, 416-422 (2020). MSC: 05C69 05C76 PDF BibTeX XML Cite \textit{B. Brešar} and \textit{M. A. Henning}, Discrete Appl. Math. 284, 416--422 (2020; Zbl 1443.05138) Full Text: DOI
Gaar, Elisabeth; Wiegele, Angelika; Krenn, Daniel; Margulies, Susan An optimization-based sum-of-squares approach to Vizing’s conjecture. (English) Zbl 1444.68303 Bradford, Russell (ed.), Proceedings of the 44th international symposium on symbolic and algebraic computation, ISSAC ’19, Beijing, China, July 15–18, 2019. New York, NY: Association for Computing Machinery (ACM). 155-162 (2019). MSC: 68W30 13P10 68R10 90C22 PDF BibTeX XML Cite \textit{E. Gaar} et al., in: Proceedings of the 44th international symposium on symbolic and algebraic computation, ISSAC '19, Beijing, China, July 15--18, 2019. New York, NY: Association for Computing Machinery (ACM). 155--162 (2019; Zbl 1444.68303) Full Text: DOI
Zerbib, Shira An improved bound in Vizing’s conjecture. (English) Zbl 1431.05118 Graphs Comb. 35, No. 6, 1401-1404 (2019). MSC: 05C69 05C76 PDF BibTeX XML Cite \textit{S. Zerbib}, Graphs Comb. 35, No. 6, 1401--1404 (2019; Zbl 1431.05118) Full Text: DOI arXiv
Lemańska, Magdalena; Tey, Joaquín; Zuazua, Rita Relations between edge removing and edge subdivision concerning domination number of a graph. (English) Zbl 1414.05229 Discrete Appl. Math. 263, 212-219 (2019). MSC: 05C69 05C40 PDF BibTeX XML Cite \textit{M. Lemańska} et al., Discrete Appl. Math. 263, 212--219 (2019; Zbl 1414.05229) Full Text: DOI arXiv
Pei, Li-Dan; Pan, Xiang-Feng; Hu, Fu-Tao Some improved inequalities related to Vizing’s conjecture. (English) Zbl 06856075 Inf. Process. Lett. 135, 85-91 (2018). MSC: 68Q PDF BibTeX XML Cite \textit{L.-D. Pei} et al., Inf. Process. Lett. 135, 85--91 (2018; Zbl 06856075) Full Text: DOI
Krop, Elliot Vizing’s conjecture: A two-thirds bound for claw-free graphs. (English) Zbl 1368.05113 Discrete Appl. Math. 230, 162-165 (2017). MSC: 05C69 05C76 PDF BibTeX XML Cite \textit{E. Krop}, Discrete Appl. Math. 230, 162--165 (2017; Zbl 1368.05113) Full Text: DOI arXiv
Brešar, Boštjan Improving the Clark-Suen bound on the domination number of the Cartesian product of graphs. (English) Zbl 1367.05155 Discrete Math. 340, No. 10, 2398-2401 (2017). MSC: 05C69 05C76 PDF BibTeX XML Cite \textit{B. Brešar}, Discrete Math. 340, No. 10, 2398--2401 (2017; Zbl 1367.05155) Full Text: DOI
Puleo, Gregory J. Maximal \(k\)-edge-colorable subgraphs, Vizing’s theorem, and Tuza’s conjecture. (English) Zbl 1361.05053 Discrete Math. 340, No. 7, 1573-1580 (2017). MSC: 05C15 PDF BibTeX XML Cite \textit{G. J. Puleo}, Discrete Math. 340, No. 7, 1573--1580 (2017; Zbl 1361.05053) Full Text: DOI arXiv
Contractor, Aziz; Krop, Elliot A class of graphs approaching Vizing’s conjecture. (English) Zbl 1416.05208 Theory Appl. Graphs 3, No. 1, Article 4, 7 p. (2016). MSC: 05C69 05C76 PDF BibTeX XML Cite \textit{A. Contractor} and \textit{E. Krop}, Theory Appl. Graphs 3, No. 1, Article 4, 7 p. (2016; Zbl 1416.05208) Full Text: DOI arXiv
Jin, Ligang; Kang, Yingli; Steffen, Eckhard Face-degree bounds for planar critical graphs. (English) Zbl 1344.05052 Electron. J. Comb. 23, No. 3, Research Paper P3.21, 11 p. (2016). MSC: 05C10 05C15 PDF BibTeX XML Cite \textit{L. Jin} et al., Electron. J. Comb. 23, No. 3, Research Paper P3.21, 11 p. (2016; Zbl 1344.05052) Full Text: Link arXiv
Krzywkowski, Marcin; Mojdeh, Doost Ali; Raoofi, Maryem Outer-2-independent domination in graphs. (English) Zbl 1333.05223 Proc. Indian Acad. Sci., Math. Sci. 126, No. 1, 11-20 (2016). MSC: 05C69 PDF BibTeX XML Cite \textit{M. Krzywkowski} et al., Proc. Indian Acad. Sci., Math. Sci. 126, No. 1, 11--20 (2016; Zbl 1333.05223) Full Text: DOI
Feng, Lihua; Cao, Jianxiang; Liu, Weijun; Ding, Shifeng; Liu, Henry The spectral radius of edge chromatic critical graphs. (English) Zbl 1330.05066 Linear Algebra Appl. 492, 78-88 (2016). MSC: 05C15 05C07 15A18 PDF BibTeX XML Cite \textit{L. Feng} et al., Linear Algebra Appl. 492, 78--88 (2016; Zbl 1330.05066) Full Text: DOI
Jin, Ligang; Kang, Yingli; Steffen, Eckhard Remarks on planar edge-chromatic critical graphs. (English) Zbl 1329.05110 Discrete Appl. Math. 200, 200-202 (2016). MSC: 05C15 05C10 PDF BibTeX XML Cite \textit{L. Jin} et al., Discrete Appl. Math. 200, 200--202 (2016; Zbl 1329.05110) Full Text: DOI arXiv
González Yero, Ismael Partial product of graphs and Vizing’s conjecture. (English) Zbl 1332.05106 Ars Math. Contemp. 9, No. 1, 19-25 (2015). Reviewer: Saeid Alikhani (Yazd) MSC: 05C69 05C76 05C70 PDF BibTeX XML Cite \textit{I. González Yero}, Ars Math. Contemp. 9, No. 1, 19--25 (2015; Zbl 1332.05106) Full Text: DOI
Brešar, Boštjan Vizing’s conjecture for graphs with domination number 3 – a new proof. (English) Zbl 1323.05099 Electron. J. Comb. 22, No. 3, Research Paper P3.38, 8 p. (2015). MSC: 05C69 05C76 PDF BibTeX XML Cite \textit{B. Brešar}, Electron. J. Comb. 22, No. 3, Research Paper P3.38, 8 p. (2015; Zbl 1323.05099) Full Text: Link
Choudhary, K.; Margulies, S.; Hicks, I. V. Integer domination of Cartesian product graphs. (English) Zbl 1309.05151 Discrete Math. 338, No. 7, 1239-1242 (2015). MSC: 05C76 05C69 05C35 PDF BibTeX XML Cite \textit{K. Choudhary} et al., Discrete Math. 338, No. 7, 1239--1242 (2015; Zbl 1309.05151) Full Text: DOI
Milanič, Martin A note on domination and independence-domination numbers of graphs. (English) Zbl 1301.05253 Ars Math. Contemp. 6, No. 1, 89-97 (2013). MSC: 05C69 05C17 68Q17 PDF BibTeX XML Cite \textit{M. Milanič}, Ars Math. Contemp. 6, No. 1, 89--97 (2013; Zbl 1301.05253) Full Text: DOI
Choudhary, K.; Margulies, S.; Hicks, I. V. A note on total and paired domination of Cartesian product graphs. (English) Zbl 1298.05245 Electron. J. Comb. 20, No. 3, Research Paper P25, 9 p. (2013). MSC: 05C69 05C76 PDF BibTeX XML Cite \textit{K. Choudhary} et al., Electron. J. Comb. 20, No. 3, Research Paper P25, 9 p. (2013; Zbl 1298.05245) Full Text: Link arXiv
Wu, Yunjian An improvement on Vizing’s conjecture. (English) Zbl 1259.05132 Inf. Process. Lett. 113, No. 3, 87-88 (2013). MSC: 05C69 PDF BibTeX XML Cite \textit{Y. Wu}, Inf. Process. Lett. 113, No. 3, 87--88 (2013; Zbl 1259.05132) Full Text: DOI arXiv
John, Niluk; Suen, Stephen Graph products and integer domination. (English) Zbl 1256.05204 Discrete Math. 313, No. 3, 217-224 (2013). MSC: 05C76 05C69 PDF BibTeX XML Cite \textit{N. John} and \textit{S. Suen}, Discrete Math. 313, No. 3, 217--224 (2013; Zbl 1256.05204) Full Text: DOI
Pilipczuk, Marcin; Pilipczuk, Michał; Škrekovski, Riste Some results on Vizing’s conjecture and related problems. (English) Zbl 1251.05126 Discrete Appl. Math. 160, No. 16-17, 2484-2490 (2012). MSC: 05C69 05C76 PDF BibTeX XML Cite \textit{M. Pilipczuk} et al., Discrete Appl. Math. 160, No. 16--17, 2484--2490 (2012; Zbl 1251.05126) Full Text: DOI
Margulies, Susan; Hicks, I. V. An algebraic exploration of dominating sets and Vizing’s conjecture. (English) Zbl 1243.05188 Electron. J. Comb. 19, No. 2, Research Paper P1, 30 p. (2012). MSC: 05C69 13P10 PDF BibTeX XML Cite \textit{S. Margulies} and \textit{I. V. Hicks}, Electron. J. Comb. 19, No. 2, Research Paper P1, 30 p. (2012; Zbl 1243.05188) Full Text: EMIS
Brešar, Boštjan; Dorbec, Paul; Goddard, Wayne; Hartnell, Bert L.; Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. Vizing’s conjecture: a survey and recent results. (English) Zbl 1234.05173 J. Graph Theory 69, No. 1-2, 46-76 (2012). MSC: 05C69 05C76 PDF BibTeX XML Cite \textit{B. Brešar} et al., J. Graph Theory 69, No. 1--2, 46--76 (2012; Zbl 1234.05173) Full Text: DOI
Khamis, S. M.; Nazzal, Kh. M. Equality in Vising’s conjecture fixing one factor of the cartesian product. (English) Zbl 1249.05287 Ars Comb. 96, 375-384 (2010). MSC: 05C69 PDF BibTeX XML Cite \textit{S. M. Khamis} and \textit{Kh. M. Nazzal}, Ars Comb. 96, 375--384 (2010; Zbl 1249.05287)
Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. Domination game and an imagination strategy. (English) Zbl 1223.05189 SIAM J. Discrete Math. 24, No. 3, 979-991 (2010). MSC: 05C57 91A43 05C69 05C76 PDF BibTeX XML Cite \textit{B. Brešar} et al., SIAM J. Discrete Math. 24, No. 3, 979--991 (2010; Zbl 1223.05189) Full Text: DOI
Cranston, Daniel W. Edge-choosability and total-choosability of planar graphs with no adjacent 3-cycles. (English) Zbl 1198.05044 Discuss. Math., Graph Theory 29, No. 1, 163-178 (2009). MSC: 05C15 05C10 05C78 PDF BibTeX XML Cite \textit{D. W. Cranston}, Discuss. Math., Graph Theory 29, No. 1, 163--178 (2009; Zbl 1198.05044) Full Text: DOI arXiv
Aharoni, Ron; Szabó, Tibor Vizing’s conjecture for chordal graphs. (English) Zbl 1211.05098 Discrete Math. 309, No. 6, 1766-1768 (2009). MSC: 05C69 PDF BibTeX XML Cite \textit{R. Aharoni} and \textit{T. Szabó}, Discrete Math. 309, No. 6, 1766--1768 (2009; Zbl 1211.05098) Full Text: DOI
Brešar, Boštjan; Rall, Douglas F. Fair reception and Vizing’s conjecture. (English) Zbl 1179.05080 J. Graph Theory 61, No. 1, 45-54 (2009). MSC: 05C69 PDF BibTeX XML Cite \textit{B. Brešar} and \textit{D. F. Rall}, J. Graph Theory 61, No. 1, 45--54 (2009; Zbl 1179.05080) Full Text: DOI
Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. Rainbow domination in graphs. (English) Zbl 1163.05046 Taiwanese J. Math. 12, No. 1, 213-225 (2008). MSC: 05C69 05C15 PDF BibTeX XML Cite \textit{B. Brešar} et al., Taiwanese J. Math. 12, No. 1, 213--225 (2008; Zbl 1163.05046) Full Text: DOI
Blidia, Mostafa; Chellali, Mustapha A note on Vizing’s generalized conjecture. (English) Zbl 1143.05317 Opusc. Math. 27, No. 2, 181-185 (2007). MSC: 05C69 PDF BibTeX XML Cite \textit{M. Blidia} and \textit{M. Chellali}, Opusc. Math. 27, No. 2, 181--185 (2007; Zbl 1143.05317)
Hou, Xinmin Total domination of Cartesian products of graphs. (English) Zbl 1134.05073 Discuss. Math., Graph Theory 27, No. 1, 175-178 (2007). MSC: 05C69 PDF BibTeX XML Cite \textit{X. Hou}, Discuss. Math., Graph Theory 27, No. 1, 175--178 (2007; Zbl 1134.05073) Full Text: DOI
El-Zahar, M. H.; Khamis, S. M.; Nazzal, Kh. M. On the domination number of the Cartesian product of the cycle of length \(n\) and any graph. (English) Zbl 1112.05074 Discrete Appl. Math. 155, No. 4, 515-522 (2007). Reviewer: Van Bang Le (Rostock) MSC: 05C69 PDF BibTeX XML Cite \textit{M. H. El-Zahar} et al., Discrete Appl. Math. 155, No. 4, 515--522 (2007; Zbl 1112.05074) Full Text: DOI
Van Wieren, Douglas M. Critical cyclic patterns related to the domination number of the torus. (English) Zbl 1119.05084 Discrete Math. 307, No. 3-5, 615-632 (2007). Reviewer: Haiko Müller (Leeds) MSC: 05C69 68R10 PDF BibTeX XML Cite \textit{D. M. Van Wieren}, Discrete Math. 307, No. 3--5, 615--632 (2007; Zbl 1119.05084) Full Text: DOI
Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. Paired-domination of Cartesian products of graphs and rainbow domination. (English) Zbl 1200.05154 Raspaud, André (ed.) et al., 7th international colloquium on graph theory, Hyeres, France, September 12–16, 2005. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 22, 233-237 (2005). MSC: 05C69 05C76 05C15 PDF BibTeX XML Cite \textit{B. Brešar} et al., Electron. Notes Discrete Math. 22, 233--237 (2005; Zbl 1200.05154) Full Text: DOI
Henning, Michael A.; Rall, Douglas F. On the total domination number of Cartesian products of graphs. (English) Zbl 1062.05109 Graphs Comb. 21, No. 1, 63-69 (2005). MSC: 05C69 05C35 PDF BibTeX XML Cite \textit{M. A. Henning} and \textit{D. F. Rall}, Graphs Comb. 21, No. 1, 63--69 (2005; Zbl 1062.05109) Full Text: DOI
Hartnell, Bert L.; Rall, Douglas F. Improving some bounds for dominating Cartesian products. (English) Zbl 1055.05115 Discuss. Math., Graph Theory 23, No. 2, 261-272 (2003). MSC: 05C69 PDF BibTeX XML Cite \textit{B. L. Hartnell} and \textit{D. F. Rall}, Discuss. Math., Graph Theory 23, No. 2, 261--272 (2003; Zbl 1055.05115) Full Text: DOI
Zhang, Limin Every planar graph with maximum degree 7 is of class 1. (English) Zbl 0988.05042 Graphs Comb. 16, No. 4, 467-495 (2000). MSC: 05C15 PDF BibTeX XML Cite \textit{L. Zhang}, Graphs Comb. 16, No. 4, 467--495 (2000; Zbl 0988.05042) Full Text: DOI
Clark, W. Edwin; Suen, Stephen An inequality related to Vizing’s conjecture. (English) Zbl 0947.05056 Electron. J. Comb. 7, No. 1, Notes N4, 3 p. (2000); printed version J. Comb. 7, No. 2 (2000). Reviewer: William G.Brown (Montréal) MSC: 05C69 05C35 PDF BibTeX XML Cite \textit{W. E. Clark} and \textit{S. Suen}, Electron. J. Comb. 7, No. 1, Research paper N4, 3 p. (2000; Zbl 0947.05056) Full Text: EMIS EuDML
Hartnell, Bert L.; Rall, Douglas F. Lower bounds for dominating Cartesian products. (English) Zbl 0938.05048 J. Comb. Math. Comb. Comput. 31, 219-226 (1999). Reviewer: Fedor Fomin (St.Peterburg) MSC: 05C69 PDF BibTeX XML Cite \textit{B. L. Hartnell} and \textit{D. F. Rall}, J. Comb. Math. Comb. Comput. 31, 219--226 (1999; Zbl 0938.05048)
Hartnell, Bert; Rall, Douglas F. Domination in Cartesian products: Vizing’s conjecture. (English) Zbl 0890.05035 Haynes, Teresa W. (ed.) et al., Domination in graphs. Advanced topics. New York, NY: Marcel Dekker. Pure Appl. Math., Marcel Dekker. 209, 163-189 (1998). Reviewer: C.Jagger (Cambridge) MSC: 05C35 PDF BibTeX XML Cite \textit{B. Hartnell} and \textit{D. F. Rall}, in: Domination in graphs. Advanced topics. New York, NY: Marcel Dekker. 163--189 (1998; Zbl 0890.05035)
Klobučar, Antoaneta Domination numbers of cardinal products of graphs. (Abstract of thesis). (English) Zbl 0890.05037 Glas. Mat., III. Ser. 32, No. 2, 348 (1997). MSC: 05C35 05C38 PDF BibTeX XML Cite \textit{A. Klobučar}, Glas. Mat., III. Ser. 32, No. 2, 348 (1997; Zbl 0890.05037)
Stiebitz, Michael; Toft, Bjarne An abstract generalization of a map reduction theorem of Birkhoff. (English) Zbl 0872.05014 J. Comb. Theory, Ser. B 65, No. 2, 165-185 (1995). Reviewer: W.Mader (Hannover) MSC: 05C15 PDF BibTeX XML Cite \textit{M. Stiebitz} and \textit{B. Toft}, J. Comb. Theory, Ser. B 65, No. 2, 165--185 (1995; Zbl 0872.05014) Full Text: DOI
Hartnell, Bert L.; Rall, Douglas F. On Vizing’s conjecture. (English) Zbl 0764.05092 Combinatorics, graph theory, and computing, Proc. 22nd Southeast Conf., Baton Rouge/LA (USA) 1991, Congr. Numerantium 82, 87-96 (1991). MSC: 05C99 PDF BibTeX XML Cite \textit{B. L. Hartnell} and \textit{D. F. Rall}, in: Proceedings of the twenty-second southeastern conference on combinatorics, graph theory, and computing, held at Louisiana State University, Baton Rouge, LA, USA, February 10-15, 1991. Winnipeg: Utilitas Mathematica Publishing Inc.. 87--96 (1991; Zbl 0764.05092)
Chetwynd, A. G.; Hilton, A. J. W. The chromatic index of graphs with large maximum degree, where the number of vertices of maximum degree is relatively small. (English) Zbl 0716.05021 J. Comb. Theory, Ser. B 48, No. 1, 45-66 (1990). Reviewer: J.Fiamčík MSC: 05C15 05C35 PDF BibTeX XML Cite \textit{A. G. Chetwynd} and \textit{A. J. W. Hilton}, J. Comb. Theory, Ser. B 48, No. 1, 45--66 (1990; Zbl 0716.05021) Full Text: DOI
Problems. (English) Zbl 0699.05001 Irregularities of partitions, Pap. Meet., Fertod/Hung. 1986, Algorithms Comb. 8, 161-165 (1989). MSC: 05-01 05Cxx 00A07 PDF BibTeX XML
Füredi, Z. The chromatic index of simple hypergraphs. (English) Zbl 0589.05036 Graphs Comb. 2, 89-92 (1986). Reviewer: I.Tomescu MSC: 05C15 05C65 05B25 PDF BibTeX XML Cite \textit{Z. Füredi}, Graphs Comb. 2, 89--92 (1986; Zbl 0589.05036) Full Text: DOI