The χ-Binding Function of d-Directional Segment Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F25%3A00144086" target="_blank" >RIV/00216224:14330/25:00144086 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00454-025-00737-2" target="_blank" >https://doi.org/10.1007/s00454-025-00737-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00454-025-00737-2" target="_blank" >10.1007/s00454-025-00737-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The χ-Binding Function of d-Directional Segment Graphs

Popis výsledku v původním jazyce

Given a positive integer d, the class d-DIR is defined as all those intersection graphs formed from a finite collection of line segments in R-2 having at most d slopes. Since each slope induces an interval graph, it easily follows for every G in d-DIR with clique number at most omega that the chromatic number chi(G) of G is at most d omega. We show for every even value of omega how to construct a graph in d-DIR that meets this bound exactly. This partially confirms a conjecture of Bhattacharya, Dvorak and Noorizadeh. Furthermore, we show that the chi-binding function of d-DIR is omega bar right arrow d omega for omega even and omega bar right arrow d(omega-1)+1 for omega odd. This extends an earlier result by Kostochka and Nesetril, which treated the special case d=2.

Název v anglickém jazyce

The χ-Binding Function of d-Directional Segment Graphs

Popis výsledku anglicky

Given a positive integer d, the class d-DIR is defined as all those intersection graphs formed from a finite collection of line segments in R-2 having at most d slopes. Since each slope induces an interval graph, it easily follows for every G in d-DIR with clique number at most omega that the chromatic number chi(G) of G is at most d omega. We show for every even value of omega how to construct a graph in d-DIR that meets this bound exactly. This partially confirms a conjecture of Bhattacharya, Dvorak and Noorizadeh. Furthermore, we show that the chi-binding function of d-DIR is omega bar right arrow d omega for omega even and omega bar right arrow d(omega-1)+1 for omega odd. This extends an earlier result by Kostochka and Nesetril, which treated the special case d=2.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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

2025

Kód důvěrnosti údajů

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

Název periodika

DISCRETE & COMPUTATIONAL GEOMETRY

ISSN

0179-5376

e-ISSN

1432-0444

Svazek periodika

74

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

758-770

Kód UT WoS článku

001489543200001

EID výsledku v databázi Scopus

2-s2.0-105005115811