Oriented coloring is NP-complete on a small class of graphs
نویسندگان
چکیده
A series of recent papers shows that it is NP-complete to decide whether an oriented graph admits a homomorphism to the tournament T4 on 4 vertices containing a 4-circuit, each time on a smaller graph class. We improve these results by showing that homomorphism to T4 is NP-complete for bipartite planar subcubic graphs of arbitrarily large fixed girth. We also show that push homomorphism is NP-complete for planar graphs with girth 9 and for bipartite planar graphs with girth 8.
منابع مشابه
Just chromatic exellence in fuzzy graphs
A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studi...
متن کاملNP-completeness results for some problems on subclasses of bipartite and chordal graphs
Extending previous NP-completeness results for the harmonious coloring problem and the pair-complete coloring problem on trees, bipartite graphs and cographs, we prove that these problems are also NP-complete on connected bipartite permutation graphs. We also study the k-path partition problem and, motivated by a recent work of Steiner [G. Steiner, On the k-path partition of graphs, Theoret. Co...
متن کاملThe harmonious coloring problem is NP-complete for interval and permutation graphs
In this paper, we prove that the harmonious coloring problem is NP-complete for connected interval and permutation graphs. 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 previo...
متن کاملSmall H-Coloring Problems for Bounded Degree Digraphs
An NP-complete coloring or homomorphism problem may become polynomial time solvable when restricted to graphs with degrees bounded by a small number, but remain NP-complete if the bound is higher. For instance, 3-colorability of graphs with degrees bounded by 3 can be decided by Brooks’ theorem, while for graphs with degrees bounded by 4, the 3-colorability problem is NP-complete. We investigat...
متن کاملHarmonious Coloring on Subclasses of Colinear Graphs
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...
متن کامل