论文信息 - Chromatic Number of ISK4-Free Graphs

Chromatic Number of ISK4-Free Graphs

A graph G is said to be ISK4-free if it does not contain any subdivision of $$K_4$$K4 as an induced subgraph. In this paper, we propose new upper bounds for the chromatic number of ISK4-free graphs and $$\{$${ISK4, triangle$$\}$$}-free graphs.

Ngoc-Khang Le

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

[4] J. A. Bondy,et al. Graph Theory , 2008, Graduate Texts in Mathematics.

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

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

[7] 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.

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

[9] Patrice Ossona de Mendez,et al. Restricted Frame Graphs and a Conjecture of Scott , 2014, Electron. J. Comb..