no code implementations • 17 Dec 2020 • Petr A. Golovach, Daniël Paulusma, Erik Jan van Leeuwen
The Induced Disjoint Paths problem is to decide if a graph $G$ with $k$ pairs of specified vertices $(s_i, t_i)$ contains $k$ mutually induced paths $P_i$ such that each $P_i$ connects $s_i$ and $t_i$.
Data Structures and Algorithms Computational Complexity Discrete Mathematics Combinatorics
no code implementations • 17 Dec 2020 • Barnaby Martin, Daniël Paulusma, Siani Smith
A graph class is hereditary if it is closed under vertex deletion.
Computational Complexity
no code implementations • 2 Aug 2020 • Konrad K. Dabrowski, François Dross, Jisu Jeong, Mamadou Moustapha Kanté, O-joung Kwon, Sang-il Oum, Daniël Paulusma
We are also able to give partial confirmation of this conjecture by proving: (1) for every tree $T$, the class of $T$-pivot-minor-free distance-hereditary graphs has bounded linear rank-width if and only if $T$ is a caterpillar; (2) for every caterpillar $T$ on at most four vertices, the class of $T$-pivot-minor-free graphs has bounded linear rank-width.
Combinatorics Discrete Mathematics
