Contracting to a Longest Path in H-Free Graphs

Walter Kern; Daniel Paulusma

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arXiv · 1810.01542

Contracting to a Longest Path in H-Free Graphs

Walter Kern·Daniel Paulusma

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Abstract

We prove two dichotomy results for detecting long paths as patterns in a given graph. The NP-hard problem Longest Induced Path is to determine the longest induced path in a graph. The NP-hard problem Longest Path Contractibility is to determine the longest path to which a graph can be contracted to. By combining known results with new results we completely classify the computational complexity of both problems for $H$-free graphs. Our main focus is on the second problem, for which we design a general contractibility technique that enables us to reduce the problem to a matching problem.

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BibTeX RIS

Walter Kern, Daniel Paulusma. 2018-10-02. Contracting to a Longest Path in H-Free Graphs. https://arxiv.org/abs/1810.01542

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