Paper by Erik D. Demaine

Reference:

Takehiro Ito, Marcin Kamiński, and Erik D. Demaine, “Reconfiguration of List Edge-Colorings in a Graph”, in Proceedings of the 11th Algorithms and Data Structures Symposium (WADS 2009), Lecture Notes in Computer Science, volume 5664, Banff, Alberta, Canada, August 21–23, 2009, pages 375–386.

BibTeX

@InProceedings{NPReconfiguration_WADS2009,
  AUTHOR        = {Takehiro Ito and Marcin Kami\'nski and Erik D. Demaine},
  TITLE         = {Reconfiguration of List Edge-Colorings in a Graph},
  BOOKTITLE     = {Proceedings of the 11th Algorithms and Data Structures
                   Symposium (WADS 2009)},
  bookurl       = {http://www.wads.org/},
  SERIES        = {Lecture Notes in Computer Science},
  seriesurl     = {http://www.springer.de/comp/lncs/},
  VOLUME        = 5664,
  ADDRESS       = {Banff, Alberta, Canada},
  MONTH         = {August 21--23},
  YEAR          = 2009,
  PAGES         = {375--386},

  doi           = {https://dx.doi.org/10.1007/978-3-642-03367-4_33},
  dblp          = {https://dblp.org/rec/conf/wads/ItoKD09},
  comments      = {This paper is also available from <A HREF="http://dx.doi.org/10.1007/978-3-642-03367-4_33">SpringerLink</A>.},
  length        = {12 pages},
  papers        = {NPReconfiguration_DAM2012; NPReconfiguration_TCS; SubsetSumReconfiguration_JOCO; NPReconfiguration_ISAAC2008},
}

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(n²) 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(n²) recolor steps.

Comments:

This paper is also available from SpringerLink.

Length:

The paper is 12 pages.

Availability:

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Related papers:

NPReconfiguration_DAM2012 (Reconfiguration of List Edge-Colorings in a Graph)

NPReconfiguration_TCS (On the Complexity of Reconfiguration Problems)

SubsetSumReconfiguration_JOCO (Approximability of the Subset Sum Reconfiguration Problem)

NPReconfiguration_ISAAC2008 (On the Complexity of Reconfiguration Problems)