List edge and list total colourings of multigraphs
Journal of Combinatorial Theory Series B
Theoretical Computer Science - Game theory meets theoretical computer science
Reconfigurations in Graphs and Grids
SIAM Journal on Discrete Mathematics
On the Complexity of Reconfiguration Problems
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
The connectivity of boolean satisfiability: computational and structural dichotomies
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Finding paths between graph colourings: pspace-completeness and superpolynomial distances
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
On the complexity of reconfiguration problems
Theoretical Computer Science
Shortest paths between shortest paths and independent sets
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Approximability of the subset sum reconfiguration problem
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
An improved sufficient condition for reconfiguration of list edge-colorings in a tree
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Complexity of independent set reconfigurability problems
Theoretical Computer Science
Reconfiguration of list edge-colorings in a graph
Discrete Applied Mathematics
The complexity of rerouting shortest paths
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
The complexity of rerouting shortest paths
Theoretical Computer Science
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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 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 ***(n 2) recolor steps.