Reconfiguration of list edge-colorings in a graph
Author(s)Ito, Takehiro; Kaminski, Marcin; Demaine, Erik D.
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We study the problem of reconfiguring one list edge-coloring of a graph into another list edge-coloring by changing one edge color at a time, while at all times maintaining a list edge-coloring, given a list of allowed colors for each edge. First we show that this problem is PSPACE-complete, even for planar graphs of maximum degree 3 and just six colors. Then we consider the problem restricted to trees. We show that any list edge-coloring can be transformed into any other under the sufficient condition that the number of allowed colors for each edge is strictly larger than the degrees of both its endpoints. This sufficient condition is best possible in some sense. Our proof yields a polynomial-time algorithm that finds a transformation between two given list edge-colorings of a tree with n vertices using O(n [superscript 2]) recolor steps. This worst-case bound is tight: we give an infinite family of instances on paths that satisfy our sufficient condition and whose reconfiguration requires Ω(n [superscript 2]) recolor steps.
11th International Symposium, WADS 2009, Banff, Canada, August 21-23, 2009. Proceedings
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Algorithms and Data Structures
Springer Berlin / Heidelberg
Ito, Takehiro, Marcin Kamiński, and Erik D. Demaine. “Reconfiguration of List Edge-Colorings in a Graph.” Algorithms and Data Structures. Ed. Frank Dehne et al. LNCS Vol. 5664. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. 375–386.
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