On the Parameterised Complexity of Induced Multipartite Graph Parameters

Ryan L. Mann; Luke Mathieson; Catherine Greenhill

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arXiv · 2004.09938

On the Parameterised Complexity of Induced Multipartite Graph Parameters

Ryan L. Mann·Luke Mathieson·Catherine Greenhill

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Abstract

We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$ and a given graph $G$, and for natural numbers $k\geq2$ and $\ell$, we must decide whether the maximum value of $p$ over all induced $k$-partite subgraphs of $G$ is at most $\ell$. We prove that this problem is W[1]-hard. Next, we consider a variant of this problem, where we must decide whether the given graph $G$ contains a sufficiently large induced $k$-partite subgraph $H$ such that $p(H)\leq\ell$. We show that for certain parameters this problem is para-NP-hard, while for others it is fixed-parameter tractable.

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Ryan L. Mann, Luke Mathieson, Catherine Greenhill. 2020-04-21. On the Parameterised Complexity of Induced Multipartite Graph Parameters. https://arxiv.org/abs/2004.09938

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