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arXiv · 1607.06864

Deciding whether there are infinitely many prime graphs with forbidden induced subgraphs

Robert Brignall·Hojin Choi·Jisu Jeong·Sang-il Oum
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Abstract

A homogeneous set of a graph $G$ is a set $X$ of vertices such that $2\le \lvert X\rvert <\lvert V(G)\rvert$ and no vertex in $V(G)-X$ has both a neighbor and a non-neighbor in $X$. A graph is prime if it has no homogeneous set. We present an algorithm to decide whether a class of graphs given by a finite set of forbidden induced subgraphs contains infinitely many non-isomorphic prime graphs.

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Robert Brignall, Hojin Choi, Jisu Jeong, Sang-il Oum. 2016-07-23. Deciding whether there are infinitely many prime graphs with forbidden induced subgraphs. https://doi.org/10.1016/j.dam.2018.10.030

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