A survey of (m, k)-colorings

Annals of Discrete Mathematics

Volumn 55, Issue C, 1993, Pages 45-57

  Frick, Marietjie ^a  

^a UNIVERSITY OF SOUTH AFRICA   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012069660     PISSN: 01675060     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0167-5060(08)70374-1     Document Type: Article

References (36)

1. Chartrand, G., Lesniak, L., Graphs and Digraphs, 2nd edition, 1986, Wadsworth & Brooks/Cole, Monterey California.
2. Brown, J., Cornell, D.G., On generalized colorings. J. Graph Theory 11 (1987), 87–99.
3. Broere, I., Frick, M., On the order of color critical graphs. Proc. Sixteenth Southeastern International Conference on Combinatorics, Graph Theory and Computing., Congr. Numer. 47 (1985), 125–130.
4. Broere, I., Frick, M., Two results on generalized chromatic numbers. Quaestiones Mathematicae 13 (1990), 183–190.
5. Broere, I., Frick, M., On the order of uniquely (k, m)-colourable graphs. Discrete Math. 82 (1990), 225–232.
6. Broere, I., Frick, M., A characterization of the sequence of generalized chromatic numbers of a graph. Alavi, Y., et al. (eds.) Graph Theory, Combinatorics and Applications: Proceedings of the Sixth Quadrennial International Conference on the Theory and Applications of Graphs, 1991, John Wiley and Sons, Inc., New York, 179–186.
7. M. Frick, Generalised Colourings of Graphs, Ph.D.-thesis, Rand Afrikaans University, Johannesburg, (1986).
8. Sachs, H., Finite graphs Recent progress in combinatorics, 1969, Academic Press, New York, 175–184 Proc. Third. Waterloo Conf. on Combinatorics.
9. Andrews, J.A., Jacobson, M.S., On a generalization of chromatic number. Proc. Sixteenth Southeastern International Conference on Combinatorics, Graph Theory and Computing, Congr. Numer. 47 (1985), 18–33.
10. Andrews, J.A., Jacobson, M.S., On a generalization of chromatic number and two kinds of Ramsey numbers. Ars Combinatoria 23 (1987), 97–102.
11. Archdeacon, D., A note on defective colorings of graphs in surfaces. J. Graph Theory, 1987, 517–519.
12. Cowen, L.J., Cowen, R.H., Woodall, D.R., Defective colorings of graphs in surfaces: partitions into subgraphs of bounded valency. J. Graph Theory 10 (1986), 187–195.
13. M. Frick and M. A. Henning, Various results on defective colorings of graphs — submitted.
14. Harary, F., Jones, K.F., Conditional Colorability II: Bipartite Variations. Proc. Sundance Cont. Combinatorics and related topics. Congr. Numer. 50 (1985), 205–218.
15. Woodall, D., Improper colourings of graphs. Nelson, R., Wilson, R.J., (eds.) Graph Colourings, 1990, Longman Scientific and Technical Pitman Research Notes in Mathematics Series.
16. Bollobás, B., Thomason, A.G., Uniquely partitionable graphs. J. London Math. Soc. 6 (1977), 403–410.
17. Cook, R.J., Point partition numbers and girth. Proc. Amer. Math. Soc. 49 (1975), 510–514.
18. Lick, D.R., White, A.T., k-degenerate graphs. Canad. J. Math 22 (1970), 1082–1096.
19. Mitchem, J., An extension of Brooks' Theorem to n-degenerate graphs. Discrete Math. 17 (1977), 291–298.
20. Simões-Pereira, J.M.S., A note on graphs with prescribed clique and point-partition numbers. J. Combinatorial Theory (B) 14 (1973), 256–258.
21. Chartrand, G., Geller, D.P., Hedetniemi, S., A generalization of the chromatic number. Proc. Comb. Phil. Soc. 64 (1968), 265–271.
22. Mycielski, J., Sur le coloriage des graphs. Colloq. Math. 3 (1955), 161–162.
23. Descartes, B., Solution to advanced problem 4526. Amer. Math. Monthly 61 (1954), 352–353.
24. Folkman, J.H., Graphs with monochromatic complete subgraphs in every edge coloring. SIAM J. Appl. Math. 18 (1970), 19–24.
25. Brooks, R.L., On coloring the nodes of a network. Proc. Cambridge Phil. Soc. 37 (1941), 194–197.
26. Lovász, L., On decompositions of graphs. Studia Sci. Math. Hungar. 1 (1966), 237–238.
27. Dirac, G.A., Graph union and chromatic number. J. London Math. Soc. 39 (1964), 451–454.
28. Ore, O., The Four-colour Problem, 1967, Academic Press, New York.
29. Harary, F., Hedetniemi, S.T., Robinson, R.W., Uniquely colorable graphs. J. Combinatorial Theory 6 (1969), 264–270.
30. Bollobás, B., Sauer, N., Uniquely colorable graphs with large girth. Can. J. Math. 28 (1976), 1340–1344.
31. Chartrand, G., Geller, D.P., On uniquely colorable planar graphs. J. Combinatorial Theory 6 (1969), 271–278.
32. Hadwiger, H., Uber eine Klassifikation der Streckenkomplexe, Vierteljahresschr. Naturforsch. Ges. Zurich 88 (1943), 133–142.
33. Dirac, G.A., A property of 4-chromatic graphs and some remarks on critical graphs. J. London Math. Soc. 27 (1972), 85–92.
34. Wagner, K., Uber eine Eigenschaft der ebenen Komplexe. Math. Ann. 114 (1937), 570–590.
35. Mader, W., Homomorphiesatze fur Graphen. Math. Ann. 178 (1968), 154–168.
36. Wagner, K., Beweiss einer Abschwachung der Hadwiger-Vermurung. Math. Ann. 153 (1964), 139–141.