The χ-Binding Function of d-Directional Segment Graphs

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
The χ-Binding Function of d-Directional Segment Graphs
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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