Reconfiguration of list edge-colorings in a graph
Name
Demaine-Reconfiguration of list.pdf
Size
166.75 KB
Format
Adobe PDF
Checksum (MD5)
2dff259da600d427e36e1ebbea653518
Author(s)
Ito, Takehiro
Kaminski, Marcin
Demaine, Erik D.
Date Issued
July 2009
Journal
Algorithms and Data Structures
Publisher
Springer Berlin / Heidelberg
Citation
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.
Version
Author's final manuscript
Abstract
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.
Description
11th International Symposium, WADS 2009, Banff, Canada, August 21-23, 2009. Proceedings
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/978-3-642-03367-4_33
