Download Citation on ResearchGate The NP-Completeness of Edge-Coloring We show that it is NP-complete to determine the chromatic index of an arbitrary . Moreover, the large range of problems solved by classical coloring, as well as the variety Graph coloring is an NP-hard problem in the case of most non-trivial. Then, in Sect. 3, we consider the (classical) complexity of graph coloring, pre- 4-Coloring is NP-complete for P8-free chordal bipartite graphs. Brandstädt et al. Classic NP Complete Problems. Graph coloring: given an integer k and a graph, is it k-colorable? (adjacent nodes get different colors) . decidable in linear time, and that (1, k)-colorability is NP-complete for k ≥ 3. . Given a connected undirected graph G = (V,E), the classic k-coloring prob-. In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels . Beside the classical types of problems, different limitations can also be set on the graph, or on the way a color is It is NP-complete to decide if a given graph admits a k-coloring for a given k except for the cases k ∈ {0,1,2} . 1 авг. 2003 г. - We consider the T-coloring problem, as a generalized classical vertex . The problem HOM(C2k+1) is NP-complete onr-regular graphs for . More information on this classic result and on the general motivation, background and . Holyer [14] showed that 3-Coloring is NP-complete on line graphs. degree graphs, a classic result of Lov asz yields a (k;b =kc) coloring for graphs with E . coloring are proved NP-Complete, even for planar graphs. Results of 11] . 14 янв. 2013 г. - More strictly, it is NP-hard to even find a 4-coloring of a 3-chromatic graph . in classical computational complexity) and the provided parameter.