Clément Dallard

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6 papers · 1 filter

math.CO2026

Determining the Complexity of Chromatic Sum in Classes Defined by a Set of Forbidden Graphs

ClÃ©ment Dallard, DaniÃ«l Paulusma, Erik Jan van Leeuwen

The Chromatic Sum problem asks, given a graph $G$ and an integer $k$ , whether $G$ admits a colouring $c$ with sum $\sum_{v \in V} c (v) \leq k$ . We study the complexity of Chromatic S…

math.CO2025

Awesome graph parameters

Kenny BeÅ¡ter Å torgel, ClÃ©ment Dallard, Vadim Lozin +2

For a graph $G$ , we denote by $I^\pm (G)$ the size of a maximum independent set and by $I ¨ (G)$ the size of a maximum clique in $G$ . Our paper lies on the edge of two lines of research,…

math.CO2025

Induced Minor Models. I. Structural Properties and Algorithmic Consequences

Nicolas Bousquet, ClÃ©ment Dallard, MaÃ«l Dumas +4

A graph $H$ is said to be an induced minor of a graph $G$ if $H$ can be obtained from $G$ by a sequence of vertex deletions and edge contractions. Equivalently, $H$ is an induced m…

math.CO2025

On minimally tough chordal graphs

ClÃ©ment Dallard, Blas FernÃ¡ndez, Gyula Y. Katona +2

Katona and Varga showed that for any rational number $t \in (1/2, 1]$ , no chordal graph is minimally $t$ -tough, while Katona and Khan characterized all minimally $t$ -tough, chordal…

math.CO2025

Layered tree-independence number and clique-based separators

Motivated by a question of Galby, Munaro, and Yang (SoCG 2023) asking whether every graph class of bounded layered tree-independence number admits clique-based separators of sublin…

math.CO2024

Treewidth versus clique number. IV. Tree-independence number of graphs excluding an induced star

Many recent works address the question of characterizing induced obstructions to bounded treewidth. In 2022, Lozin and Razgon completely answered this question for graph classes de…