TY - GEN

T1 - Finding a path in group-labeled graphs with two labels forbidden

AU - Kawase, Yasushi

AU - Kobayashi, Yusuke

AU - Yamaguchi, Yutaro

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-662-47672-7_65

DO - 10.1007/978-3-662-47672-7_65

M3 - Conference contribution

AN - SCOPUS:84950118409

SN - 9783662476710

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 797

EP - 809

BT - Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings

A2 - Halldorsson, Magnus M.

A2 - Kobayashi, Naoki

A2 - Speckmann, Bettina

A2 - Iwama, Kazuo

PB - Springer Verlag

T2 - 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015

Y2 - 6 July 2015 through 10 July 2015

ER -