List edge and list total colorings of planar graphs without non-induced 7-cycles

Aijun Dong; Guizhen Liu; Guojun Li

doi:10.46298/dmtcs.629

Article

List edge and list total colorings of planar graphs without non-induced 7-cycles

Aijun Dong⁽¹⁾, Guizhen Liu⁽²⁾, Guojun Li⁽²⁾

(1) School of science [Shandong]

(2) School of Mathematics [Shandong]

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November 21, 2010

Published on

March 12, 2013

Last modified on

March 31, 2025

Volume 15

vol. 15:1

Graph and Algorithms

DOI

10.46298/dmtcs.629

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https://about.hal.science/hal-authorisation-v1

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List edge and list total colorings of planar graphs without non-induced 7-cycles

Aijun Dong⁽¹⁾, Guizhen Liu⁽²⁾, Guojun Li⁽²⁾

(1) School of science [Shandong]

(2) School of Mathematics [Shandong]

Abstract

Giving a planar graph G, let χ'l(G) and χ''l(G) denote the list edge chromatic number and list total chromatic number of G respectively. It is proved that if G is a planar graph without non-induced 7-cycles, then χ'l(G)≤Δ(G)+1 and χ''l(G)≤Δ(G)+2 where Δ(G)≥7.

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