Subdivisions of four blocks cycles in digraphs with large chromatic number

2021 ◽  
Vol 305 ◽  
pp. 71-75
Author(s):  
Darine Al-Mniny
Keyword(s):  
Chromatic Number ◽  
Four Blocks ◽  
Large Chromatic Number

scholarly journals Induced subgraphs of graphs with large chromatic number. XI. Orientations

2019 ◽  
Vol 76 ◽  
pp. 53-61 ◽  
Author(s):  
Maria Chudnovsky ◽  
Alex Scott ◽  
Paul Seymour
Keyword(s):  
Chromatic Number ◽  
Induced Subgraphs ◽  
Large Chromatic Number

Uniquely Colourable Graphs with Large Girth

1976 ◽  
Vol 28 (6) ◽  
pp. 1340-1344 ◽  
Author(s):  
Béla Bollobás ◽  
Norbert Sauer
Keyword(s):  
Chromatic Number ◽  
Large Girth ◽  
Large Chromatic Number

Tutte [1], writing under a pseudonym, was the first to prove that a graph with a large chromatic number need not contain a triangle. The result was rediscovered by Zykov [5] and Mycielski [4]. Erdös [2] proved the much stronger result that for every k ≧ 2 and g there exist a k-chromatic graph whose girth is at least g.

scholarly journals Induced subgraphs of graphs with large chromatic number. VIII. Long odd holes

2020 ◽  
Vol 140 ◽  
pp. 84-97 ◽  
Author(s):  
Maria Chudnovsky ◽  
Alex Scott ◽  
Paul Seymour ◽  
Sophie Spirkl
Keyword(s):  
Chromatic Number ◽  
Induced Subgraphs ◽  
Large Chromatic Number

scholarly journals Triangle-free intersection graphs of line segments with large chromatic number

2014 ◽  
Vol 105 ◽  
pp. 6-10 ◽  
Author(s):  
Arkadiusz Pawlik ◽  
Jakub Kozik ◽  
Tomasz Krawczyk ◽  
Michał Lasoń ◽  
Piotr Micek ◽  
...  
Keyword(s):  
Chromatic Number ◽  
Intersection Graphs ◽  
Line Segments ◽  
Large Chromatic Number

scholarly journals Induced Subgraphs of Graphs with Large Chromatic Number IX: Rainbow Paths

10.37236/6768 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Alex Scott ◽  
Paul Seymour
Keyword(s):  
Recent Result ◽  
Chromatic Number ◽  
Clique Number ◽  
Induced Subgraphs ◽  
Induced Subgraph ◽  
Large Chromatic Number ◽  
Vertex Colouring

We prove that for all integers $\kappa, s\ge 0$ there exists $c$ with the following property. Let $G$ be a graph with clique number at most $\kappa$ and chromatic number more than $c$. Then for every vertex-colouring (not necessarily optimal) of $G$, some induced subgraph of $G$ is an $s$-vertex path, and all its vertices have different colours. This extends a recent result of Gyárfás and Sárközy (2016) who proved the same for graphs $G$ with $\kappa=2$ and girth at least five.

scholarly journals Cycles in triangle-free graphs of large chromatic number

COMBINATORICA ◽  
2016 ◽  
Vol 37 (3) ◽  
pp. 481-494 ◽  
Author(s):  
Alexandr Kostochka ◽  
Benny Sudakov ◽  
Jacques Verstraëte
Keyword(s):  
Chromatic Number ◽  
Large Chromatic Number
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