TY - GEN

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

AU - Ito, Takehiro

AU - Kawamura, Kazuto

AU - Zhou, Xiao

PY - 2011/5/13

Y1 - 2011/5/13

N2 - We study the problem of reconfiguring one list edge-coloring 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 edge-coloring, given a list of allowed colors for each edge. Ito, Kamiński 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 edge-coloring 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 edge-coloring, given a list of allowed colors for each edge. Ito, Kamiński 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.

UR - http://www.scopus.com/inward/record.url?scp=79955747577&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955747577&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-20877-5_10

DO - 10.1007/978-3-642-20877-5_10

M3 - Conference contribution

AN - SCOPUS:79955747577

SN - 9783642208768

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

SP - 94

EP - 105

BT - Theory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Proceedings

T2 - 8th Annual Conference on Theory and Applications of Models of Computation, TAMC 2011

Y2 - 23 May 2011 through 25 May 2011

ER -