Contracting to a Longest Path in H-Free Graphs
Data Structures and Algorithms
2018-10-04 v1 Computational Complexity
Discrete Mathematics
Combinatorics
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 -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.
Cite
@article{arxiv.1810.01542,
title = {Contracting to a Longest Path in H-Free Graphs},
author = {Walter Kern and Daniel Paulusma},
journal= {arXiv preprint arXiv:1810.01542},
year = {2018}
}