Romain Bourneuf

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20242026

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cs.DM2026

Sample compression schemes for balls in structurally sparse graphs

Romain Bourneuf, JÄdrzej Hodor, Piotr Micek +1

Sample compression schemes were defined by Littlestone and Warmuth (1986) as an abstraction of the structure underlying many learning algorithms. In a sample compression scheme, we…

cs.DM2025

A Dense Neighborhood Lemma: Applications of Partial Concept Classes to Domination and Chromatic Number

In its Euclidean form, the Dense Neighborhood Lemma (DNL) asserts that if $V$ is a finite set of points of $R^{N}$ such that for each $v \in V$ the ball $B (v, 1)$ intersects…

cs.DM2025

Bounded twin-width graphs are polynomially $I ¨ $ -bounded

We show that every graph with twin-width $t$ has chromatic number $O (I ¨ ^{k_{t}})$ for some integer $k_{t}$ , where $I ¨ $ denotes the clique number. This extends a quasi-polynomial bound…

Sample compression schemes for balls in structurally sparse graphs

A Dense Neighborhood Lemma: Applications of Partial Concept Classes to Domination and Chromatic Number

Bounded twin-width graphs are polynomially I¨-bounded

Bounded twin-width graphs are polynomially $I ¨ $ -bounded