Bounds for the b-chromatic Number of Induced Subgraphs and G − e

2015 ◽  
pp. 111-116
Author(s):  
P. Francis ◽  
S. Francis Raj
Keyword(s):  
Chromatic Number ◽  
Induced Subgraphs

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

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 Large Induced Subgraphs with All Degrees Odd

1992 ◽  
Vol 1 (4) ◽  
pp. 335-349 ◽  
Author(s):  
A. D. Scott
Keyword(s):  
Chromatic Number ◽  
Random Graphs ◽  
Connected Graph ◽  
Analogous Problem ◽  
Induced Subgraphs ◽  
Induced Subgraph

We prove that every connected graph of order n ≥ 2 has an induced subgraph with all degrees odd of order at least cn/log n, where cis a constant. We also give a bound in terms of chromatic number, and resolve the analogous problem for random graphs.

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 Circular chromatic number of induced subgraphs of Kneser graphs

2018 ◽  
Vol 15 (1) ◽  
pp. 161-172
Author(s):  
Meysam Alishahi ◽  
Ali Taherkhani
Keyword(s):  
Chromatic Number ◽  
Induced Subgraphs ◽  
Circular Chromatic Number ◽  
Kneser Graphs

scholarly journals Induced Subgraphs of Graphs With Large Chromatic Number. X. Holes of Specific Residue

COMBINATORICA ◽  
2019 ◽  
Vol 39 (5) ◽  
pp. 1105-1132 ◽  
Author(s):  
Alex Scott ◽  
Paul Seymour
Keyword(s):  
Chromatic Number ◽  
Induced Subgraphs ◽  
Large Chromatic Number
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