Abstract
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(n 2) 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(n 2) recoloring steps.
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References
Bonsma, P., Cereceda, L.: Finding paths between graph colourings: PSPACE-completeness and superpolynomial distances. Theoretical Computer Science 410, 5215–5226 (2009)
Borodin, O.V., Kostochka, A.V., Woodall, D.R.: List edge and list total colourings of multigraphs. J. Combinatorial Theory, B 71, 184–204 (1997)
Gopalan, P., Kolaitis, P.G., Maneva, E.N., Papadimitriou, C.H.: The connectivity of Boolean satisfiability: computational and structural dichotomies. SIAM J. Computing 38, 2330–2355 (2009)
Hearn, R.A., Demaine, E.D.: PSPACE-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation. Theoretical Computer Science 343, 72–96 (2005)
Ito, T., Demaine, E.D., Harvey, N.J.A., Papadimitriou, C.H., Sideri, M., Uehara, R., Uno, Y.: On the complexity of reconfiguration problems. Theoretical Computer Science 412, 1054–1065 (2011)
Ito, T., Kamiński, M., Demaine, E.D.: Reconfiguration of list edge-colorings in a graph. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 375–386. Springer, Heidelberg (2009)
Jensen, T.R., Toft, B.: Graph Coloring Problems. Wiley Interscience, New York (1995)
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Ito, T., Kawamura, K., Zhou, X. (2011). An Improved Sufficient Condition for Reconfiguration of List Edge-Colorings in a Tree. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_10
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DOI: https://doi.org/10.1007/978-3-642-20877-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20876-8
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