List Edge Coloring of Planar Graphs without 6-Cycles with Two Chords
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 199-211.

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A graph G is edge-L-colorable if for a given edge assignment L = L(e) : e ∈ E(G), there exists a proper edge-coloring φ of G such that φ(e) ∈ L(e) for all e ∈ E(G). If G is edge-L-colorable for every edge assignment L such that |L(e)| ≥ k for all e ∈ E(G), then G is said to be edge-k-choosable. In this paper, we prove that if G is a planar graph without 6-cycles with two chords, then G is edge-k-choosable, where k = max7, Δ(G) + 1, and is edge-t-choosable, where t = max9, Δ(G).
Keywords: planar graph, edge choosable, list edge chromatic number, chord
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Hu, Linna; Sun, Lei; Wu, Jian-Liang. List Edge Coloring of Planar Graphs without 6-Cycles with Two Chords. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 199-211. http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a12/

[1] M. Bonamy, Planar graphs with Δ ≥ 8 are (Δ+1)-edge-choosable, SIAM J. Discrete Math. 29 (2015) 1735–1763. doi: 10.1137/130927449

[2] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (North-Holland, New York, 1976).

[3] O.V. Borodin, An extension of Kotzig's theorem and the list edge coloring of planar graphs, Mat. Zametki 48 (1990) 22–48.

[4] O.V. Borodin, A.V. Kostochka and D.R. Woodall, List edge and list total colourings of multigraphs, J. Combin. Theory Ser. B 71 (1997) 184–204. doi: 10.1006/jctb.1997.1780

[5] J.S. Cai, J.F. Hou, X. Zhang and G.Z. Liu, Edge-choosability of planar graphs without non-induced 5-cycles, Inform. Process. Lett. 109 (2009) 343–346. doi: 10.1016/j.ipl.2008.12.001

[6] J.S. Cai, List edge coloring of planar graphs without non-induced 6-cycles, Graphs Combin. 31 (2015) 827–832. doi: 10.1007/s00373-014-1420-6

[7] F. Galvin, The list chromatic index of a bipartite multigraph, J. Combin. Theory Ser. B 63 (1995) 153–158. doi: 10.1006/jctb.1995.1011

[8] R. Hägkvist and J. Janssen, New bounds on the list-chromatic index of the complete graph and other simple graphs, Combin. Probab. Comput. 6 (1997) 295–313. doi: 10.1017/S0963548397002927

[9] R. Hägkvist and A. Chetwynd, Some upper bounds on the total and list chromatic numbers of multigraphs, J. Graph Theory 16 (1992) 503–516. doi: 10.1002/jgt.3190160510

[10] A.J. Harris, Problems and conjectures in extrema graph theory, Ph.D. Dissertation (Cambridge University, UK, 1984).

[11] J.F. Hou, G.Z. Liu and J.S. Cai, List edge and list total colorings of planar graphs without 4- cycles, Theoret. Comput. Sci. 369 (2006) 250–255. doi: 10.1016/j.tcs.2006.08.043

[12] J.F. Hou, G.Z. Liu and J.S. Cai, Edge-choosability of planar graphs without adjacent triangles or without 7-cycles, Discrete Math. 309 (2009) 77–84. doi: 10.1016/j.disc.2007.12.046

[13] T.R. Jensen and B. Toft, Graph Coloring Problems (Wiley, New York, 1995).

[14] M. Juvan, B. Mohar and R. Šrekovski, Graphs of degree 4 are 5-choosable, J. Graph Theory 32 (1999) 250–262. doi: 10.1002/(SICI)1097-0118(199911)32:3(250::AID-JGT5)3.0.CO;2-R

[15] A.V. Kostochka, List edge chromatic number of graphs with large girth, Discrete Math. 101 (1992) 189-201. doi: 10.1016/0012-365X(92)90602-C

[16] B. Liu, J.F. Hou and G.Z. Liu, List edge and list total colorings of planar graphs without short cycles, Inform. Process. Lett. 108 (2008) 347–351. doi: 10.1016/j.ipl.2008.07.003

[17] Y. Shen, G. Zheng, W. He and Y. Zhao, Structural properties and edge choosability of planar graphs without 4- cycles, Discrete Math. 308 (2008) 5789–5794. doi: 10.1016/j.disc.2007.09.048

[18] W.F. Wang and K.W. Lih, Structural properties and edge choosability of planar graphs without 6-cycles, Combin. Probab. Comput. 10 (2001) 267–276.

[19] W.F. Wang and K.W. Lih, Choosability, edge choosability and total choosability of outerplanar graphs, European J. Combin. 22 (2001) 71–78. doi: 10.1006/eujc.2000.0430

[20] W.F. Wang and K.W. Lih, Choosability and edge choosability of planar graphs without five cycles, Appl. Math. Lett. 15 (2002) 561–565. doi: 10.1016/S0893-9659(02)80007-6

[21] J.L. Wu and P. Wang, List-edge and list-total colorings of graphs embedded on hyperbolic surfaces, Discrete Math. 308 (2008) 6210–6215. doi: 10.1016/j.disc.2007.11.044

[22] L. Zhang and B. Wu, Edge choosability of planar graphs without small cycles, Discrete Math. 283 (2004) 289–293. doi: 10.1016/j.disc.2004.01.001