Intersection graphs of paths in a tree
Journal of Combinatorial Theory Series B
Labeling algorithms for domination problems in sun-free chordal graphs
Discrete Applied Mathematics
Achromatic number is NP-complete for cographs and interval graphs
Information Processing Letters
Finding dominating cliques efficiently, in strongly chordal graphs and undirected path graphs
Discrete Mathematics - Topics on domination
A faster algorithm to recognize undirected path graphs
Discrete Applied Mathematics
The complexity of harmonious colouring for trees
Discrete Applied Mathematics - Special issue: Combinatorial Optimization 1992 (CO92)
Some results on the achromatic number
Journal of Graph Theory
Graph classes: a survey
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
NP-completeness results for some problems on subclasses of bipartite and chordal graphs
Theoretical Computer Science
Linear colorings of simplicial complexes and collapsing
Journal of Combinatorial Theory Series A
Note: The harmonious coloring problem is NP-complete for interval and permutation graphs
Discrete Applied Mathematics
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
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Given a simple graph G, a harmonious coloring of G is a proper vertex coloring such that each pair of colors appears together on at most one edge. The harmonious chromatic number is the least integer k for which G admits a harmonious coloring with k colors. Extending previous NP-completeness results of the harmonious coloring problem on subclasses of chordal and co-chordal graphs, we prove that the problem remains NP-complete for split undirected path graphs; we also prove that the problem is NP-complete for colinear graphs by showing that split undirected path graphs form a subclass of colinear graphs. Moreover, we provide a polynomial solution for the harmonious coloring problem for the class of split strongly chordal graphs, the interest of which lies on the fact that the problem has been proved to be NP-complete on both split and strongly chordal graphs.