Recent progress on strong edge-coloring of graphs

A strong edge-coloring of a graph G = (V,E) is a partition of its edge set E into induced matchings. In this paper, we gave a short survey on recent results about strong edge-coloring of a graph.

[1]  Hong Zhu,et al.  On strong list edge coloring of subcubic graphs , 2014, Discret. Math..

[2]  Andreas Brandstädt,et al.  Maximum Induced Matchings for Chordal Graphs in Linear Time , 2008, Algorithmica.

[3]  Udi Rotics,et al.  Finding Maximum Induced Matchings in Subclasses of Claw-Free and P5-Free Graphs, and in Graphs with Matching and Induced Matching of Equal Maximum Size , 2003, Algorithmica.

[4]  Guanghui Wang,et al.  Strong list-chromatic index of subcubic graphs , 2018, Discret. Math..

[5]  Oleg V. Borodin,et al.  Precise Upper Bound for the Strong Edge Chromatic Number of Sparse Planar Graphs , 2013, Discuss. Math. Graph Theory.

[6]  Maksim Maydanskiy The incidence coloring conjecture for graphs of maximum degree 3 , 2005, Discret. Math..

[7]  Moshe Lewenstein,et al.  New results on induced matchings , 2000, Discret. Appl. Math..

[8]  Alan M. Frieze,et al.  The Strong Chromatic Index of Random Graphs , 2005, SIAM J. Discret. Math..

[9]  Felix Joos Induced Matchings in Graphs of Bounded Maximum Degree , 2016, SIAM J. Discret. Math..

[10]  Mohammad Mahdian On the computational complexity of strong edge coloring , 2002, Discret. Appl. Math..

[11]  Tao Wang,et al.  Odd graph and its applications to the strong edge coloring , 2014, Appl. Math. Comput..

[12]  Lily Chen,et al.  Strong edge-coloring for planar graphs with large girth , 2019, Discret. Math..

[13]  Kittikorn Nakprasit,et al.  A note on the strong chromatic index of bipartite graphs , 2008, Discret. Math..

[14]  Hervé Hocquard,et al.  Strong edge-colouring of sparse planar graphs , 2014, Discret. Appl. Math..

[15]  Andreas Brandstädt,et al.  The induced matching and chain subgraph cover problems for convex bipartite graphs , 2007, Theor. Comput. Sci..

[16]  Henning Bruhn,et al.  A stronger bound for the strong chromatic index , 2015, Electron. Notes Discret. Math..

[17]  Richard A. Brualdi,et al.  Incidence and strong edge colorings of graphs , 1993, Discret. Math..

[18]  Jou-Ming Chang,et al.  Induced matchings in asteroidal triple-free graphs , 2003, Discret. Appl. Math..

[19]  William T. Trotter,et al.  Induced matchings in cubic graphs , 1993, J. Graph Theory.

[20]  Dieter Rautenbach,et al.  Induced Matchings in Subcubic Graphs , 2014, SIAM J. Discret. Math..

[21]  Micha Dbski Fractional strong chromatic index of bipartite graphs , 2017 .

[22]  Alexandr V. Kostochka,et al.  Strong chromatic index of subcubic planar multigraphs , 2015, Eur. J. Comb..

[23]  Daniel W. Cranston Strong edge-coloring of graphs with maximum degree 4 using 22 colors , 2006, Discret. Math..

[24]  Tao Wang,et al.  Strong chromatic index of k-degenerate graphs , 2013, Discret. Math..

[25]  André Raspaud,et al.  Strong Chromatic Index Of Planar Graphs With Large Girth , 2013, Discuss. Math. Graph Theory.

[26]  Hervé Hocquard,et al.  Strong edge colouring of subcubic graphs , 2011, Discret. Appl. Math..

[27]  David Manlove,et al.  On the approximability of the maximum induced matching problem , 2005, J. Discrete Algorithms.

[28]  Barry Guiduli On incidence coloring and star arboricity of graphs , 1997, Discret. Math..

[29]  Malgorzata Sleszynska-Nowak Clique number of the square of a line graph , 2016, Discret. Math..

[30]  Vijay V. Vazirani,et al.  NP-Completeness of Some Generalizations of the Maximum Matching Problem , 1982, Inf. Process. Lett..

[31]  Roman Soták,et al.  Strong edge-coloring of planar graphs , 2014, Discret. Math..

[32]  Zsolt Tuza,et al.  The maximum number of edges in 2K2-free graphs of bounded degree , 1990, Discret. Math..

[33]  Martin Charles Golumbic,et al.  Irredundancy in Circular Arc Graphs , 1993, Discret. Appl. Math..

[34]  André Raspaud,et al.  Strong edge-colorings of sparse graphs with large maximum degree , 2016, Eur. J. Comb..

[35]  Bruce A. Reed,et al.  A Bound on the Strong Chromatic Index of a Graph, , 1997, J. Comb. Theory B.

[36]  Kathie Cameron,et al.  Induced Matchings in Intersection Graphs , 2000, Electron. Notes Discret. Math..

[37]  Yue Zhao,et al.  Planar Graphs of Maximum Degree Seven are Class I , 2001, J. Comb. Theory B.

[38]  Gexin Yu,et al.  Strong edge-colorings for $$k$$k-degenerate graphs , 2012, Graphs Comb..

[39]  Marthe Bonamy,et al.  Strong edge coloring sparse graphs , 2015, Electron. Notes Discret. Math..

[40]  Luke Postle,et al.  On the clique number of the square of a line graph and its relation to maximum degree of the line graph , 2019, J. Graph Theory.

[41]  Mohammad Mahdian,et al.  The strong chromatic index of C 4 -free graphs , 2000 .

[42]  Xiangqian Zhou,et al.  The strong chromatic index of (3, Δ)-bipartite graphs , 2017, Discret. Math..

[43]  Kathie Cameron,et al.  Finding a maximum induced matching in weakly chordal graphs , 2003, Discret. Math..

[44]  Gerard J. Chang,et al.  On the precise value of the strong chromatic index of a planar graph with a large girth , 2015, Discret. Appl. Math..

[45]  Angelika Steger,et al.  On induced matchings , 1993, Discret. Math..

[46]  Wensong Lin,et al.  The strong chromatic index of a class of graphs , 2008, Discret. Math..

[47]  Gerard J. Chang,et al.  Strong edge-coloring for jellyfish graphs , 2015, Discret. Math..

[48]  Michal Debski On a topological relaxation of a conjecture of Erdős and Nešetřil , 2015, Eur. J. Comb..

[49]  Limin Zhang,et al.  Every Planar Graph with Maximum Degree 7 Is of Class 1 , 2000, Graphs Comb..

[50]  Min Chen,et al.  Planar graphs with maximum degree 4 are strongly 19-edge-colorable , 2018, Discret. Math..

[51]  Jaroslaw Grytczuk,et al.  The strong chromatic index of sparse graphs , 2015, Inf. Process. Lett..

[52]  Rémi de Joannis de Verclos,et al.  Colouring squares of claw-free graphs , 2017, Electron. Notes Discret. Math..

[53]  Vadim V. Lozin On maximum induced matchings in bipartite graphs , 2002, Inf. Process. Lett..

[54]  Xiangwen Li,et al.  On strong edge-coloring of graphs with maximum degree 4 , 2018, Discret. Appl. Math..

[55]  Felix Joos,et al.  Induced Matchings in Graphs of Degree at Most 4 , 2016, SIAM J. Discret. Math..

[56]  Aurélie Lagoutte,et al.  Strong edge-coloring of $(3, \Delta)$-bipartite graphs , 2014, 1412.2624.

[57]  Lars Døvling Anderson The strong chromatic index of a cubic graph is at most 10 , 1992 .

[58]  Gerard J. Chang,et al.  Strong Chromatic Index of 2‐Degenerate Graphs , 2013, J. Graph Theory.

[59]  Michele Zito Induced Matchings in Regular Graphs and Trees , 1999, WG.