Odd Chromatic Number of Graph Classes

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00370168" target="_blank" >RIV/68407700:21240/23:00370168 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/978-3-031-43380-1_4" target="_blank" >https://doi.org/10.1007/978-3-031-43380-1_4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-43380-1_4" target="_blank" >10.1007/978-3-031-43380-1_4</a>

Result language

angličtina

Original language name

Odd Chromatic Number of Graph Classes

Original language description

A graph is called odd (respectively, even) if every vertex has odd (respectively, even) degree. Gallai proved that every graph can be partitioned into two even induced subgraphs, or into an odd and an even induced subgraph. We refer to a partition into odd subgraphs as an odd colouring of G. Scott [Graphs and Combinatorics, 2001] proved that a graph admits an odd colouring if and only if it has an even number of vertices. We say that a graph G is k-odd colourable if it can be partitioned into at most k odd induced subgraphs. We initiate the systematic study of odd colouring and odd chromatic number of graph classes. In particular, we consider for a number of classes whether they have bounded odd chromatic number. Our main results are that interval graphs, graphs of bounded modular-width and graphs of bounded maximum degree all have bounded odd chromatic number.

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Proceedings of the 49th International Workshop on Graph-Theoretic Concepts in Computer Science

ISBN

978-3-031-43379-5

ISSN

0302-9743

e-ISSN

1611-3349

Number of pages

15

Pages from-to

44-58

Publisher name

Springer

Place of publication

Cham

Event location

Fribourg

Event date

Jun 28, 2023

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

001162209000004