Graph Theory II 1 Coloring GraphsDevadas, SriniLehman, EricNotes, Lecture
Computational Complexity: The problem of finding the total chromatic number is NP-hard in general, meaning there is no known fast algorithm to solve the problem for all types of graphs. Large Graphs: As the size of a graph increases, the computational complexity of finding the total chromatic ...
The maximum number of edges in an F-free n-vertex graph is denoted by ex(n,F) and the n-vertex graphs that achieve this bound are called F-extremal. Turán has found the value of ex(n,F) for the case where F is a clique Kk on k vertices, for any k≥3. Moreover, he showed...
Journal of Graph TheoryM. Basavaraju, L. S. Chandran, Acyclic edge coloring of graphs with maxi- mum degree 4, arXiv:0801.1744v1, Jan. 2008.Basavaraju M,Chandran L S.Acyclic edge coloring of graphs with maximum degree 4. Journal of Graph Theory . 2009...
Journal of Graph TheoryA. Nakamoto, K. Noguchi, and K. Ozeki, Cyclic 4-colorings of graphs on surfaces, submitted.A. Nakamoto, K. Noguchi and K. Ozeki, Cyclic 4-colorings of graphs on surfaces, J. Graph Theory 82 (2016), 265-278....
We complement these results by proving that graphs with all cycle lengths divisible by 3 are 3-colorable in a strongly proper connected sense. Theorem 3. Let G be a 2-connected graph. If the length of every cycle in G is divisible by 3, then spc(G) ≤ 3. The proof of this result...
In fact, it is shown in [18] that deciding whether a graph admits a b-coloring with a given number of colors is an NP-complete problem, even for connected bipartite graphs. The following upper bound for the b-chromatic number of a graph, presented in [13], has been proved to be ...
An experimental investigation of iterated local search for coloring graphs. In: Cagnoni S, Gottlieb J, Hart E, Middendorf M, Raidl G, editors. Applications of evolutionary computing, Proceedings of EvoWorkshops2002: EvoCOP, EvoIASP, EvoSTim, Kinsale, Ireland, vol. 2279. Berlin: Springer; 3-...
Graph coloring Incidence coloring Maximum average degree Incidence chromatic number 1. Introduction In the following we only consider simple, non-empty connected graphs. In a graph G=(V,E), an incidence is an edge e coupled with one of its two extremities, denoted by (u,uv) or (v,uv)....
2005, Science in China, Series A: Mathematics Vertex-distinguishing edge colorings of graphs 2003, Journal of Graph Theory View all citing articles on Scopus 1 Partially supported by NSF grant DMS-9971788 and DARPA grant F33615-01-C-1900. ...