Odd Chromatic Number of Graph Classes

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Odd Chromatic Number of Graph Classes

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Odd Chromatic Number of Graph Classes

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

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

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název statě ve sborníku

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

Počet stran výsledku

15

Strana od-do

44-58

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Fribourg

Datum konání akce

28. 6. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001162209000004