A note on the star chromatic number
Journal of Graph Theory
Good and semi-strong colorings of oriented planar graphs
Information Processing Letters
Acyclic and oriented chromatic numbers of graphs
Journal of Graph Theory
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Circular chromatic number: a survey
Discrete Mathematics
Construction of sparse graphs with prescribed circular colorings
Discrete Mathematics
The circular chromatic number of series-parallel graphs of large odd girth
Discrete Mathematics
SIAM Journal on Discrete Mathematics
Two algorithms for general list matrix partitions
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Full Constraint Satisfaction Problems
SIAM Journal on Computing
Adapted List Coloring of Graphs and Hypergraphs
SIAM Journal on Discrete Mathematics
An upper bound on adaptable choosability of graphs
European Journal of Combinatorics
Adapted game colouring of graphs
European Journal of Combinatorics
An asymptotically tight bound on the adaptable chromatic number
Journal of Graph Theory
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The adaptable chromatic number of a graph G is the smallest integer k such that for any edge k-colouring of G there exists a vertex k-colouring of G in which the same colour never appears on an edge and both its endpoints. (Neither the edge nor the vertex colourings are necessarily proper in the usual sense.) We give an efficient characterization of graphs with adaptable chromatic number at most two, and prove that it is NP-hard to decide if a given graph has adaptable chromatic number at most k, for any k=3. The adaptable chromatic number cannot exceed the chromatic number; for complete graphs, the adaptable chromatic number seems to be near the square root of the chromatic number. On the other hand, there are graphs of arbitrarily high girth and chromatic number, in which the adaptable chromatic number coincides with the classical chromatic number. In analogy with well-known properties of chromatic numbers, we also discuss the adaptable chromatic numbers of planar graphs, and of graphs with bounded degree, proving a Brooks-like result.