论文信息 - The Chromatic Number of Graphs with No Induced Subdivision of K4

The Chromatic Number of Graphs with No Induced Subdivision of K4

In 2012, Leveque, Maffray and Trotignon conjectured that if a graph does not contain an induced subdivision of $$K_4$$, then it is 4-colorable. Recently, Le showed that every such graph is 24-colorable. In this paper, we improve the upper bound to 8.

Qinghai Liu | Guantao Chen | Qing Cui | Xing Feng | Yuan Chen

[1] William T. Trotter,et al. Triangle-free intersection graphs of line segments with large chromatic number , 2012, J. Comb. Theory, Ser. B.

[2] Chun-Hung Liu,et al. Triangle-free graphs that do not contain an induced subdivision of K4 are 3-colorable , 2019, J. Graph Theory.

[3] Nicolas Trotignon,et al. On graphs with no induced subdivision of K4 , 2012, J. Comb. Theory, Ser. B.

[4] Alex Scott. Induced trees in graphs of large chromatic number , 1997 .

[5] Daniela Kühn,et al. Induced Subdivisions In Ks,s-Free Graphs of Large Average Degree , 2004, Comb..

[6] Ngoc-Khang Le. Chromatic Number of ISK4-Free Graphs , 2017, Graphs Comb..

[7] A. Gyárfás. Problems from the world surrounding perfect graphs , 1987 .

[8] Nicolas Trotignon,et al. On Triangle-Free Graphs That Do Not Contain a Subdivision of the Complete Graph on Four Vertices as an Induced Subgraph , 2017, J. Graph Theory.