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Title of Journal: J Comb Optim

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Abbravation: Journal of Combinatorial Optimization

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Springer US

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DOI

10.1007/s13391-014-3293-5

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1573-2886

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Total coloring of planar graphs without adjacent s

Authors: Huijuan Wang Bin Liu Yan Gu Xin Zhang Weili Wu Hongwei Gao
Publish Date: 2015/09/16
Volume: 33, Issue: 1, Pages: 265-274
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Abstract

In the study of computer science optimization computation of Hessians matrix graph coloring is an important tool In this paper we consider a classical coloring total coloring Let G=VE be a graph Total coloring is a coloring of Vcup E such that no two adjacent or incident elements vertex/edge receive the same color Let G be a planar graph with varDelta ge 8 We proved that if for every vertex vin V there exists two integers i vj vin 34567 such that v is not incident with adjacent i vcycles and j vcycles then the total chromatic number of graph G is varDelta +1This work was supported in part by the National Natural Science Foundation of China under Grants 11301410 11401386 11402075 11501316 71171120 71571108 the Projects of International Regional Cooperation and Exchanges of NSFC 71411130215 the Specialized Research Fund for the Doctoral Program of Higher Education 20133706110002 China Postdoctoral Science Foundation under Grants 2015M570568 2015M570572 and the Shandong Provincial Natural Science Foundation of China under Grants ZR2014AQ001 ZR2015GZ007

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