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Approximately Coloring Graphs Without Long Induced Paths

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approximately-coloring.pdf (337.83 KB)

Date

2019

Authors

Chudnovsky, Maria
Schaudt, Oliver
Spirkl, Sophie
stein, maya
Zhong, Mingxian

Journal Title

Journal ISSN

Volume Title

Publisher

Springer Nature

Abstract

It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on t vertices, for fixed t. We propose an algorithm that, given a 3-colorable graph without an induced path on t vertices, computes a coloring with max{5,2⌈t−12⌉−2} many colors. If the input graph is triangle-free, we only need max{4,⌈t−12⌉+1} many colors. The running time of our algorithm is O((3t−2+t2)m+n) if the input graph has n vertices and m edges.

Description

This is a post-peer-review, pre-copyedit version of an article published in Algorithmica. The final authenticated version is available online at: https://doi.org/10.1007/s00453-019-00577-6

Keywords

graph coloring, forbidden induced paths, approximation algorithm

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Citation

URI

https://doi.org/10.1007/s00453-019-00577-6
 http://hdl.handle.net/10012/18519

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Waterloo Research
Combinatorics and Optimization