Finding a path in group-labeled graphs with two labels forbidden

Yasushi Kawase, Yusuke Kobayashi, Yutaro Yamaguchi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

The parity of the length of paths and cycles is a classical and well-studied topic in graph theory and theoretical computer science. The parity constraints can be extended to the label constraints in a group-labeled graph, which is a directed graph with a group label on each arc. Recently, paths and cycles in group-labeled graphs have been investigated, such as finding non-zero disjoint paths and cycles. In this paper, we present a solution to finding an s–t path in a grouplabeled graph with two labels forbidden. This also leads to an elementary solution to finding a zero path in a Z3-labeled graph, which is the first nontrivial case of finding a zero path. This situation in fact generalizes the 2-disjoint paths problem in undirected graphs, which also motivates us to consider that setting. More precisely, we provide a polynomial-time algorithm for testing whether there are at most two possible labels of s–t paths in a group-labeled graph or not, and finding s–t paths attaining at least three distinct labels if exist. We also give a necessary and sufficient condition for a group-labeled graph to have exactly two possible labels of s–t paths, and our algorithm is based on this characterization.

Original languageEnglish
Title of host publicationAutomata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings
EditorsMagnus M. Halldorsson, Naoki Kobayashi, Bettina Speckmann, Kazuo Iwama
PublisherSpringer Verlag
Pages797-809
Number of pages13
ISBN (Print)9783662476710
DOIs
Publication statusPublished - Jan 1 2015
Externally publishedYes
Event42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 - Kyoto, Japan
Duration: Jul 6 2015Jul 10 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9134
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference42nd International Colloquium on Automata, Languages and Programming, ICALP 2015
CountryJapan
CityKyoto
Period7/6/157/10/15

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Kawase, Y., Kobayashi, Y., & Yamaguchi, Y. (2015). Finding a path in group-labeled graphs with two labels forbidden. In M. M. Halldorsson, N. Kobayashi, B. Speckmann, & K. Iwama (Eds.), Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings (pp. 797-809). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9134). Springer Verlag. https://doi.org/10.1007/978-3-662-47672-7_65