Graph coloring is an important tool in the study of optimization, computer science, network design, e.g., file transferring in a computer network, pattern matching, computation of Hessians matrix and so on. In this pa...Graph coloring is an important tool in the study of optimization, computer science, network design, e.g., file transferring in a computer network, pattern matching, computation of Hessians matrix and so on. In this paper, we consider one important coloring, vertex coloring of a total graph, which is also called total coloring. We consider a planar graph G with maximum degree △（G） 〉 8, and proved that if G contains no adjacent i,j-cycles with two chords for some i,j E {5,6,7}, then G is total-（△ ＋ 1）-colorable.展开更多
LetGbe a planar graph with maximum degreeΔ.In this paper,we prove that if any4-cycle is not adjacent to ani-cycle for anyi∈{3,4}in G,then the list edge chromatic numberχl（G）=Δand the list total chromatic number...LetGbe a planar graph with maximum degreeΔ.In this paper,we prove that if any4-cycle is not adjacent to ani-cycle for anyi∈{3,4}in G,then the list edge chromatic numberχl（G）=Δand the list total chromatic numberχl（G）=Δ＋1.展开更多
基金Supported by National Natural Science Foundation of China(Grants Nos.11401386,11402075,11501316,71171120 and 71571180)China Postdoctoral Science Foundation(Grants Nos.2015M570568,2015M570572)+2 种基金the Qingdao Postdoctoral Application Research Project(Grants Nos.2015138,2015170)the Shandong Provincial Natural Science Foundation of China(Grants Nos.ZR2013AM001,ZR2014AQ001,ZR2015GZ007,ZR2015FM023)the Scientific Research Program of the Higher Education Institution of Xinjiang(Grant No.XJEDU20141046)
文摘Graph coloring is an important tool in the study of optimization, computer science, network design, e.g., file transferring in a computer network, pattern matching, computation of Hessians matrix and so on. In this paper, we consider one important coloring, vertex coloring of a total graph, which is also called total coloring. We consider a planar graph G with maximum degree △（G） 〉 8, and proved that if G contains no adjacent i,j-cycles with two chords for some i,j E {5,6,7}, then G is total-（△ ＋ 1）-colorable.
基金Supported by National Natural Science Foundation of China(Grant Nos.11201440 and 11271006)Graduate Independent Innovation Foundation of Shandong University(Grant No.yzc12100)
文摘LetGbe a planar graph with maximum degreeΔ.In this paper,we prove that if any4-cycle is not adjacent to ani-cycle for anyi∈{3,4}in G,then the list edge chromatic numberχl（G）=Δand the list total chromatic numberχl（G）=Δ＋1.
