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 • 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 • 4 Feb 2021 • Júlio Araújo, Marin Bougeret, Victor A. Campos, Ignasi Sau
In the Maximum Minimal Vertex Cover (MMVC) problem, we are given a graph $G$ and a positive integer $k$, and the objective is to decide whether $G$ contains a minimal vertex cover of size at least $k$.
Data Structures and Algorithms Computational Complexity 05C15 G.2.2; F.2.2
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
