J4 ›› 2009, Vol. 44 ›› Issue (10): 17-20.

• Articles • Previous Articles     Next Articles

List edge and list total colorings of planar graphs with adjacent triangles

 DONG Ai-Jun, LI Guo-Jun, JU Jing-Song   

  1. School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Received:2009-03-24 Online:2009-10-16 Published:2009-12-07

PDF (PC)

1059

Abstract:

Given a planar graph G，let G,χ´l(G)andχ"l(G)denote the list edge chromatic number and list total chromatic number of  G respectively. It is proved that if a planar graph G withΔ(G)≥7 such that a triangle is adjacent to at most one triangle,then χ´l(G)≤Δ(G)+1and χ"l(G)≤Δ(G)+2

Key words: triangle; list edge chromatic number; list total chromatic number

CLC Number: 

  • O157.5
[1] . On the Smarandachelyadjacentvertex edge coloring of some double graphs [J]. J4, 2009, 44(12): 25-29.
[2] WANG Chao. A degree condition for graphs to have Hamiltonian (g,f)-factors [J]. J4, 2009, 44(10): 21-25.
[3] LIU Shen-Sheng, SHU Zhi-Jiang. An upper bound on the vertex distinguishing IE total chromatic number of graphs [J]. J4, 2009, 44(10): 14-16.
[4] JU Jing-Song, LI Shuo, YANG Xin-Gang. Degree conditions for bipartite graphs to contain 6-cycles [J]. J4, 2009, 44(8): 13-15.
[5] YUAN Xiu-Hua. Signed edge total domination numbers of graphs [J]. J4, 2009, 44(8): 21-24.
[6] LIU Hai-Yang, MA Cheng-Gang, WANG Zhi-Beng. Graham's conjecture on the product of the thorn graph [J]. J4, 2009, 44(8): 25-30.
[7] GAO Yu-Fen, WEI Xiao-Li. On the extremal Merrifield-Simmons index with  respect to trees having given number of endvertices [J]. J4, 2009, 44(8): 16-20.
[8] DUAN Ci-Meng, LV Ping-Li, MIAO Lian-Yang, MIAO Zheng-Ke. L(2,1,1)-Labeling of simple graphs [J]. J4, 2009, 44(8): 31-34.
[9] LIU Xiao-Yan. null [J]. J4, 2008, 43(12): 28-30.
[10] GENG Jian-yan,YAN Jin,LI Feng . Vertex-disjoint 4-cycle in a bipartite graph [J]. J4, 2008, 43(5): 87-92 .
[11] PAN Rui-xia,LAN Mei,LIU Gui-zhen . A condition of isolated toughness on the existence of fractional ［a,b］-factors of graphs [J]. J4, 2008, 43(5): 93-96 .
[12] 林丽美1,2,周书明1,2,许力1,2. t／t-diagnosability and diagnosis algorithm on hierarchical cubic network [J]. J4, 2013, 48(7): 85-92.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd