English

Scott's induced subdivision conjecture for maximal triangle-free graphs

Combinatorics 2011-07-19 v1
Authors: Nicolas Bousquet , Stéphan Thomassé
View on arXiv ↗ PDF ↗

Abstract

Scott conjectured that the class of graphs with no induced subdivision of a given graph is χ\chi-bounded. We verify his conjecture for maximal triangle-free graphs.

Keywords

hadwiger conjecture graph theory

Cite

@article{arxiv.1107.3491,
  title  = {Scott's induced subdivision conjecture for maximal triangle-free graphs},
  author = {Nicolas Bousquet and Stéphan Thomassé},
  journal= {arXiv preprint arXiv:1107.3491},
  year   = {2011}
}

Related papers

View all related →
Combinatorics · Mathematics
A positive instance of Scott's Conjecture on induced subdivisions
Kathie Cameron, Ni Luh Dewi Sintiari, Sophie Spirkl
2026-02-13
Combinatorics · Mathematics
On Scott's odd induced subgraph conjecture and a related problem
Bo Ning
2026-04-22
Combinatorics · Mathematics
On triangle-free graphs that do not contain a subdivision of the complete graph on four vertices as an induced subgraph
Nicolas Trotignon, Kristina Vušković
2020-12-01
Combinatorics · Mathematics
Chi-boundedness of graphs containing no cycles with $k$ chords
Joonkyung Lee, Shoham Letzter, Alexey Pokrovskiy
2025-09-03
Combinatorics · Mathematics
Restricted frame graphs and a conjecture of Scott
Jérémie Chalopin, Louis Esperet, Zhentao Li, Patrice Ossona de Mendez
2022-03-03
Combinatorics · Mathematics
Triangle-free graphs that do not contain an induced subdivision of $K_4$ are 3-colorable
Maria Chudnovsky, Chun-Hung Liu, Oliver Schaudt, Sophie Spirkl +2
2023-10-31
Combinatorics · Mathematics
Three-coloring triangle-free graphs without long forbidden paths
Yidong Zhou, Jorik Jooken, Baoyuan Shan, Jan Goedgebeur +1
2025-12-24
Combinatorics · Mathematics
Induced subdivisions and bounded expansion
Zdeněk Dvořák
2017-06-20
Combinatorics · Mathematics
Induced subgraphs of graphs with large chromatic number. VII. Gy\'arf\'as' complementation conjecture
Alex Scott, Paul Seymour
2019-03-15
Combinatorics · Mathematics
Maximum odd induced subgraph of a graph concerning its chromatic number
Tao Wang, Baoyindureng Wu
2024-02-27
Combinatorics · Mathematics
Excluding induced subdivisions of the bull and related graphs
Maria Chudnovsky, Irena Penev, Alexander Scott, Nicolas Trotignon
2013-09-06
Discrete Mathematics · Computer Science
Claw-free graphs, skeletal graphs, and a stronger conjecture on $\omega$, $\Delta$, and $\chi$
Andrew D. King, Bruce A. Reed
2012-12-14
Combinatorics · Mathematics
Odd induced subgraphs in graphs with treewidth at most two
Xinmin Hou, Lei Yu, Jiaao Li, Boyuan Liu
2017-07-18
Combinatorics · Mathematics
Induced trees in triangle-free graphs
Jiri Matousek, Robert Samal
2007-12-03
Combinatorics · Mathematics
A note on large induced subgraphs with prescribed residues in bipartite graphs
Zach Hunter
2022-01-04
Combinatorics · Mathematics
A counterexample to a conjecture about triangle-free induced subgraphs of graphs with large chromatic number
Alvaro Carbonero, Patrick Hompe, Benjamin Moore, Sophie Spirkl
2022-09-16
Combinatorics · Mathematics
Chi-boundedness of graph classes excluding wheel vertex-minors
Hojin Choi, O-joung Kwon, Sang-il Oum, Paul Wollan
2019-01-16
Combinatorics · Mathematics
Structure and colour in triangle-free graphs
N. R. Aravind, Stijn Cambie, Wouter Cames van Batenburg, Rémi de Joannis de Verclos +2
2020-03-17
Discrete Mathematics · Computer Science
Chromatic number of ISK4-free graphs
Ngoc Khang Le
2016-11-15
Combinatorics · Mathematics
Forbidden induced subgraphs for perfectness of claw-free graphs of independence number at least 4
Christoph Brause, Trung Duy Doan, Přemysl Holub, Adam Kabela +3
2021-09-03
Combinatorics · Mathematics
Borodin-Kostochka conjecture for a family of $P_6$-free graphs
Di Wu, Rong Wu
2025-04-29
Combinatorics · Mathematics
Rooted induced trees in triangle-free graphs
Florian Pfender
2008-12-15
Combinatorics · Mathematics
Identifying codes in triangle-free graphs of bounded maximum degree
Dipayan Chakraborty, Florent Foucaud, Michael A. Henning, Tuomo Lehtilä
2024-07-24
Combinatorics · Mathematics
Nucleation-free independent graphs with implied nonedges
Jialong Cheng, Meera Sitharam, Ileana Streinu, William Sims
2025-08-19
Combinatorics · Mathematics
Typical structure of hereditary graph families. II. Exotic examples
Sergey Norin, Yelena Yuditsky
2020-07-03
R2 v1 2026-06-21T18:38:23.361Z