Generalized colorings of outerplanar and planar graphs
Graph theory with applications to algorithms and computer science
Generalized colorings of graphs
Graph theory with applications to algorithms and computer science
The subchromatic number of a graph
Discrete Mathematics - Graph colouring and variations
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
On the NP-completeness of the k-colorability problem for triangle-free graphs
Discrete Mathematics
The complexity of G-free colourability
Proceedings of an international symposium on Graphs and combinatorics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Planar Graph Coloring with Forbidden Subgraphs: Why Trees and Paths Are Dangerous
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Computing
On 2-subcolourings of chordal graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
The hypocoloring problem: complexity and approximability results when the chromatic number is small
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
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In a graph coloring, each color class induces a disjoint union of isolated vertices. A graph subcoloring generalizes this concept, since here each color class induces a disjoint union of complete graphs. Erd?os and independently Albertson et al. proved that every graph of maximum degree at most 3 has a 2-subcoloring. We point out in this paper that this fact is best possible with respect to degree-constraints by showing that the problem of recognizing 2-subcolorable graphs with maximum degree 4 is NP-complete, even when restricted to triangle-free planar graphs. Moreover, in general, for fixed k, recognizing k-subcolorable graphs is NP-complete on graphs with maximum degree at most k2. In contrast, we show that, for arbitrary k, k-SUBCOLORABILITY can be computed efficiently on graphs of bounded treewidth and on cographs.