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no code implementations • 11 Mar 2021 • Julien Baste, Ignasi Sau, Dimitrios M. Thilikos

${\cal F}$-TM-DELETION) problem consists in, given a graph $G$ and an integer $k$, decide whether there exists $S \subseteq V(G)$ with $|S| \leq k$ such that $G \setminus S$ does not contain any of the graphs in ${\cal F}$ as a minor (resp.

Data Structures and Algorithms Computational Complexity Discrete Mathematics Combinatorics 05C85, 68R10, 05C75, 05C83, 05C75, 05C69 G.2.2; F.2.2

no code implementations • 11 Mar 2021 • Julien Baste, Ignasi Sau, Dimitrios M. Thilikos

In particular, we prove that when ${\cal F}$ contains a single connected graph $H$ that is either $P_5$ or is not a minor of the banner (that is, the graph consisting of a $C_4$ plus a pendent edge), then $f_{{\cal F}}(tw)= 2^{\Omega(tw \cdot \log tw)}$.

Data Structures and Algorithms Computational Geometry Discrete Mathematics Combinatorics 05C85, 68R10, 05C75, 05C83, 05C75, 05C69 G.2.2; F.2.2

no code implementations • 2 Mar 2021 • Öznur Yaşar Diner, Archontia C. Giannopoulou, Giannos Stamoulis, Dimitrios M. Thilikos

We show that, for every non-trivial hereditary class ${\cal G}$, the problem of deciding whether $G\in{\cal G}^{(k)}$ is NP-complete.

Discrete Mathematics Data Structures and Algorithms Combinatorics 05C75, 05C83, 05C75, 05C69 G.2.2; F.2.2

no code implementations • 26 Feb 2021 • Fedor V. Fomin, Petr A. Golovach, Dimitrios M. Thilikos

Facilitator wins if his agents meet in some vertex of the graph.

Discrete Mathematics Computational Complexity Data Structures and Algorithms 05C85 G.2.2

no code implementations • 16 Apr 2020 • Stratis Limnios, George Dasoulas, Dimitrios M. Thilikos, Michalis Vazirgiannis

As a multipartite graph is a combination of bipartite graphs, that are in turn the incidence graphs of hypergraphs, we design k-hypercore decomposition, the hypergraph analogue of k-core degeneracy.

no code implementations • 9 Jul 2019 • Julien Baste, Ignasi Sau, Dimitrios M. Thilikos

For a fixed finite collection of graphs ${\cal F}$, the ${\cal F}$-M-DELETION problem asks, given an $n$-vertex input graph $G,$ for the minimum number of vertices that intersect all minor models in $G$ of the graphs in ${\cal F}$.

Data Structures and Algorithms Computational Complexity Combinatorics 05C85, 68R10, 05C75, 05C83, 05C75, 05C69 G.2.2; F.2.2

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