TY - GEN

T1 - The parity hamiltonian cycle problem in directed graphs

AU - Nishiyama, Hiroshi

AU - Yamauchi, Yukiko

AU - Kijima, Shuji

AU - Yamashita, Masafumi

N1 - Funding Information:
This work is partly supported by JSPS KAKENHI Grant Number 15K15938, 25700002, 15H02666, and Grant-in-Aid for Scientific Research on Innovative Areas MEXT Japan “Exploring the Limits of Computation (ELC).”
Publisher Copyright:
© Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - This paper investigates a variant of the Hamiltonian cycle, the parity Hamiltonian cycle (PHC) problem: a PHC in a directed graph is a closed walk (possibly using an arc more than once) which visits every vertex odd number of times. Nishiyama et al. (2015) investigated the undirected version of the PHC problem, and gave a simple characterization that a connected undirected graph has a PHC if and only if it has even order or it is non-bipartite. This paper gives a complete characterization when a directed graph has a PHC, and shows that the PHC problem in a directed graph is solved in polynomial time. The characterization, unlike with the undirected case, is described by a linear system over GF(2).

AB - This paper investigates a variant of the Hamiltonian cycle, the parity Hamiltonian cycle (PHC) problem: a PHC in a directed graph is a closed walk (possibly using an arc more than once) which visits every vertex odd number of times. Nishiyama et al. (2015) investigated the undirected version of the PHC problem, and gave a simple characterization that a connected undirected graph has a PHC if and only if it has even order or it is non-bipartite. This paper gives a complete characterization when a directed graph has a PHC, and shows that the PHC problem in a directed graph is solved in polynomial time. The characterization, unlike with the undirected case, is described by a linear system over GF(2).

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U2 - 10.1007/978-3-319-45587-7_5

DO - 10.1007/978-3-319-45587-7_5

M3 - Conference contribution

AN - SCOPUS:84988028711

SN - 9783319455860

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

SP - 50

EP - 58

BT - Combinatorial Optimization - 4th International Symposium, ISCO 2016, Revised Selected Papers

A2 - Fujishige, Satoru

A2 - Mahjoub, Ridha A.

A2 - Cerulli, Raffaele

PB - Springer Verlag

T2 - 4th International Symposium on Combinatorial Optimization, ISCO 2016

Y2 - 16 May 2016 through 18 May 2016

ER -