Sep 12, 2023 · We show that the \chi-binding function of d-DIR is \omega \mapsto d\omega for \omega even and \omega \mapsto d(\omega-1)+1 for \omega odd.
Furthermore, we show that the $\chi$-binding function of $d$-DIR is $\omega \mapsto d\omega$ for $\omega$ even and $\omega \mapsto d(\omega-1)+1$ for $\omega$ ...
Sep 12, 2023 · 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 R2 ...
Sep 12, 2023 · Furthermore, we show that the χ -binding function of d -DIR is ω ↦ d ω for ω even and ω ↦ d ( ω − 1 ) + 1 for ω odd. This refutes said ...
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 ${\mathbb ...
Nov 10, 2023 · In general, there are no upper bounds on χ in terms of ω. The graphs for which we can approximate the chromatic number with ω ≤ χ ≤ f(ω) for ...
This partially confirms a conjecture of Bhattacharya, Dvořák and Noorizadeh. Furthermore, we show that the χ-binding function of d-DIR is ω↦ dω for ω even and ...
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The χ-binding function of d-directional segment graphs. Combinatorics, Graph Theory, and Ordered Sets, Faculty of Mathematics and Information Science ...
Nov 17, 2023 · The χ-binding function of d-directional segment graphs. ven. 10 ... χ is lower-bounded by the clique number ω. In general, there are no ...