On Coloring Resilient Graphs

Jeremy Kun; Lev Reyzin

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arXiv · 1402.4376

On Coloring Resilient Graphs

Jeremy Kun·Lev Reyzin

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Abstract

We introduce a new notion of resilience for constraint satisfaction problems, with the goal of more precisely determining the boundary between NP-hardness and the existence of efficient algorithms for resilient instances. In particular, we study $r$-resiliently $k$-colorable graphs, which are those $k$-colorable graphs that remain $k$-colorable even after the addition of any $r$ new edges. We prove lower bounds on the NP-hardness of coloring resiliently colorable graphs, and provide an algorithm that colors sufficiently resilient graphs. We also analyze the corresponding notion of resilience for $k$-SAT. This notion of resilience suggests an array of open questions for graph coloring and other combinatorial problems.

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Jeremy Kun, Lev Reyzin. 2014-02-18. On Coloring Resilient Graphs. https://arxiv.org/abs/1402.4376

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