Respected readers, authors and reviewers, you can add comments to this page on any questions about the contribution, review, editing and publication of this journal. We will give you an answer as soon as possible. Thank you for your support!
WANG Xiao. The chromatic number for fork-free graphs[J]. Journal of East China Normal University (Natural Sciences), 2016, (1): 102-106. doi: 10.3969/j.issn.1000-5641.2016.01.0051
Citation:
WANG Xiao. The chromatic number for fork-free graphs[J]. Journal of East China Normal University (Natural Sciences), 2016, (1): 102-106. doi: 10.3969/j.issn.1000-5641.2016.01.0051
WANG Xiao. The chromatic number for fork-free graphs[J]. Journal of East China Normal University (Natural Sciences), 2016, (1): 102-106. doi: 10.3969/j.issn.1000-5641.2016.01.0051
Citation:
WANG Xiao. The chromatic number for fork-free graphs[J]. Journal of East China Normal University (Natural Sciences), 2016, (1): 102-106. doi: 10.3969/j.issn.1000-5641.2016.01.0051
Randerath once conjectured that every triangle-free and fork-free graph is 3-colourable. By a lemma, the conjecture for C_4-free graphs was proved.Moreover, the result that every triangle-free, C_4-free and C_{2,2,1,n}-free graph is (n+2)-colourable was proved as well, where C_{2,2,1,n} is the long handled fork with order (n+6) obtained from E-graph and P_n by joining the center vertex of E and one endvertex of P_n.
[1]REINHARD D. Graph Theorey (Second Edition) [M]. Hong Kong:Springer-Verlag, 2000: 95-117.[2]GY\'{A]RF\'{A]S A. Problems from the world surrounding perfect graphs [J]. Zastow Mat, 1987, 19: 413-441.[3]WAGON S. A bound on the chromatic number of graphs without certain induced subgraphs [J]. J of Combin Theory, Series B, 1980, 29(3):345-346.[4]GY\'{A]RF\'{A]S A, SZEMER\'{E]DI E and Tuza. Induced subtrees ingraphs of large chromatic number [J]. Discrete Math, 1980, 30(3):235-244.[5] DUAN F and WU B Y. On chromatic number of graphs without certain induced subgraph [J]. Ars combinatoria, 2011, 101: 33-34.[6] DUAN F and ZHANG W J. On chromatic number of $\{2K_1+K_2, C_4\]$-free graphs [J]. Journal of East China Normal University: Natural Science, 2014(1): 9-12.[7] RANDERATH B, SCHIERMEYER I. A note on Brooks' theorem for triangle-free graphs [J]. Australas J Comb, 2002, 26: 3-9.[8] RANDERATH B, SCHIERMEYER I. Vertex coloring and forbidden subgraphs-a survey [J]. Graphs Combin, 2004, 20(1): 1-40.[9] RANDERATH B. The Vizing bound for the chromatic number based on forbidden pairs [D]. Nordrhein-Westfalen: RWTH Aachen University, 1998.[10] FAN G, XU B, YE T, et al. Forbidden subgraphs and 3-colorings [J]. Siam J Disc Math, 2014, 28: 1226-1256.