TY - GEN

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

AU - Kawase, Yasushi

AU - Kobayashi, Yusuke

AU - Yamaguchi, Yutaro

N1 - Funding Information:
Y. Kawase—Supported by JSPS KAKENHI Grant Number 26887014. Y. Kobayashi—Supported by JST, ERATO, Kawarabayashi Large Graph Project, and by JSPS KAKENHI Grant Number 24106002, 24700004. Y. Yamaguchi—Supported by JSPS Fellowship for Young Scientists.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

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 -