TY - JOUR

T1 - An improved sufficient condition for reconfiguration of list edge-colorings in a tree

AU - Ito, Takehiro

AU - Kawamura, Kazuto

AU - Zhou, Xiao

PY - 2012/3

Y1 - 2012/3

N2 - We study the problem of reconfiguring one list edgecoloring of a graph into another list edge-coloring by changing only one edge color assignment at a time, while at all times maintaining a list edgecoloring, given a list of allowed colors for each edge. Ito, Kamínski and Demaine gave a sufficient condition so that any list edge-coloring of a tree can be transformed into any other. In this paper, we give a new sufficient condition which improves the known one. Our sufficient condition is best possible in some sense. The proof is constructive, and yields a polynomial-time algorithm that finds a transformation between two given list edge-colorings of a tree with n vertices via O(n2) recoloring steps. We remark that the upper bound O(n 2) on the number of recoloring steps is tight, because there is an infinite family of instances on paths that satisfy our sufficient condition and whose reconfiguration requires Ω(n2) recoloring steps.

AB - We study the problem of reconfiguring one list edgecoloring of a graph into another list edge-coloring by changing only one edge color assignment at a time, while at all times maintaining a list edgecoloring, given a list of allowed colors for each edge. Ito, Kamínski and Demaine gave a sufficient condition so that any list edge-coloring of a tree can be transformed into any other. In this paper, we give a new sufficient condition which improves the known one. Our sufficient condition is best possible in some sense. The proof is constructive, and yields a polynomial-time algorithm that finds a transformation between two given list edge-colorings of a tree with n vertices via O(n2) recoloring steps. We remark that the upper bound O(n 2) on the number of recoloring steps is tight, because there is an infinite family of instances on paths that satisfy our sufficient condition and whose reconfiguration requires Ω(n2) recoloring steps.

KW - Graph algorithm

KW - List edge-coloring

KW - Reachability on solution space

KW - Reconfiguration problem

KW - Tree

UR - http://www.scopus.com/inward/record.url?scp=84863239866&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863239866&partnerID=8YFLogxK

U2 - 10.1587/transinf.E95.D.737

DO - 10.1587/transinf.E95.D.737

M3 - Article

AN - SCOPUS:84863239866

VL - E95-D

SP - 737

EP - 745

JO - IEICE Transactions on Information and Systems

JF - IEICE Transactions on Information and Systems

SN - 0916-8532

IS - 3

ER -