Fractional Coloring Planar Graphs under Steinberg-type Conditions  

作　　者：Xiao Lan HU Jia Ao LI 

机构地区：[1]School of Mathematics and Statistics&Hubei Key Laboratory of Mathematical Sciences,Central China Normal University,Wuhan 430079,P.R.China [2]School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第5期904-922,共19页数学学报（英文版）

基　　金：partially supported by the National Natural Science Foundation of China(Grant No.11971196);Hubei Provincial Science and Technology Innovation Base(Platform)Special Project 2020DFH002;the second author was partially supported by the National Natural Science Foundation of China(Grant Nos.11901318,12131013);the Young Elite Scientists Sponsorship Program by Tianjin(Grant No.TJSQNTJ-2020-09)。

摘　　要：A Steinberg-type conjecture on circular coloring is recently proposed that for any prime p≥5,every planar graph of girth p without cycles of length from p+1 to p(p-2)is Cp-colorable(that is,it admits a homomorphism to the odd cycle Cp).The assumption of p≥5 being prime number is necessary,and this conjecture implies a special case of Jaeger’s Conjecture that every planar graph of girth 2p-2 is Cp-colorable for prime p≥5.In this paper,combining our previous results,we show the fractional coloring version of this conjecture is true.Particularly,the p=5 case of our fractional coloring result shows that every planar graph of girth 5 without cycles of length from 6 to 15 admits a homomorphism to the Petersen graph.

关 键 词：Fractional coloring circular coloring planar graphs GIRTH HOMOMORPHISM 

分 类 号：O157.5[理学—数学]