TY - GEN

T1 - The complexity of (list) edge-coloring reconfiguration problem

AU - Osawa, Hiroki

AU - Suzuki, Akira

AU - Ito, Takehiro

AU - Zhou, Xiao

N1 - Funding Information:
This work is partially supported by JSPS KAKENHI Grant Numbers JP26730001 (A. Suzuki), JP15H00849 and JP16K00004 (T. Ito), and JP16K00003 (X. Zhou).
Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

N2 - Let G be a graph such that each edge has its list of available colors, and assume that each list is a subset of the common set consisting of k colors. Suppose that we are given two list edge-colorings f0 and fr of G, and asked whether there exists a sequence of list edge-colorings of G between f0 and fr such that each list edge-coloring can be obtained from the previous one by changing a color assignment of exactly one edge. This problem is known to be PSPACE-complete for every integer k ≥ 6 and planar graphs of maximum degree three, but any computational hardness was unknown for the non-list variant in which every edge has the same list of k colors. In this paper, we first improve the known result by proving that, for every integer k ≥ 4, the problem remains PSPACE-complete even for planar graphs of maximum degree three and bounded bandwidth. Since the problem is known to be solvable in polynomial time if k ≤ 3, our result gives a sharp analysis of the complexity status with respect to the number k of colors. We then give the first computational hardness result for the non-list variant: for every integer k ≥ 5, the nonlist variant is PSPACE-complete even for planar graphs of maximum degree k and bandwidth linear in k.

AB - Let G be a graph such that each edge has its list of available colors, and assume that each list is a subset of the common set consisting of k colors. Suppose that we are given two list edge-colorings f0 and fr of G, and asked whether there exists a sequence of list edge-colorings of G between f0 and fr such that each list edge-coloring can be obtained from the previous one by changing a color assignment of exactly one edge. This problem is known to be PSPACE-complete for every integer k ≥ 6 and planar graphs of maximum degree three, but any computational hardness was unknown for the non-list variant in which every edge has the same list of k colors. In this paper, we first improve the known result by proving that, for every integer k ≥ 4, the problem remains PSPACE-complete even for planar graphs of maximum degree three and bounded bandwidth. Since the problem is known to be solvable in polynomial time if k ≤ 3, our result gives a sharp analysis of the complexity status with respect to the number k of colors. We then give the first computational hardness result for the non-list variant: for every integer k ≥ 5, the nonlist variant is PSPACE-complete even for planar graphs of maximum degree k and bandwidth linear in k.

UR - http://www.scopus.com/inward/record.url?scp=85014195108&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014195108&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-53925-6_27

DO - 10.1007/978-3-319-53925-6_27

M3 - Conference contribution

AN - SCOPUS:85014195108

SN - 9783319539249

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

SP - 347

EP - 358

BT - WALCOM

A2 - Rahman, Md. Saidur

A2 - Yen, Hsu-Chun

A2 - Poon, Sheung-Hung

PB - Springer Verlag

T2 - 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017

Y2 - 29 March 2017 through 31 March 2017

ER -