Coloring graph products - A survey

Discrete Mathematics

Volumn 155, Issue 1-3, 1996, Pages 135-145

  Klavžar, Sandi ^a  

^a UNIVERSITY OF MARIBOR   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010169953     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0012-365x(94)00377-u     Document Type: Article

References (45)

1. M. Borowiecki, On chromatic number of products of two graphs, Colloq. Math. 25 (1972) 49-52.
2. S.A. Burr, P. Erdös and L. Lovász, On graphs of Ramsey type, Ars Combin. 1 (1976) 167-190.
3. N. Čižek and S. Klavžar, On the chromatic number of the lexicographic product and the Cartesian sum of graphs, Discrete Math. 134 (1994) 17-24.
4. D. Duffus, B. Sands and R.E. Woodrow, On the chromatic number of the product of graphs, J. Graph Theory 9 (1985) 487-495.
5. M. El-Zahar and N.W. Sauer, The chromatic number of the product of two 4-chromatic graphs is 4, Combinatorica 5 (1985) 121-126.
6. J. Feigenbaum and A.A. Schäffer, Finding the prime factors of strong direct product graphs in polynomial time, Discrete Math. 109 (1992) 77-102.
7. M.R. Garey and D.S. Johnson, The complexity of near-optimal graph coloring, J. Assoc. Comput. Mach. 23 (1976) 43-49.
8. D. Geller, r-tuple colorings of uniquely colorable graphs, Discrete Math. 16 (1976) 9-12.
9. D. Geller and S. Stahl, The chromatic number and other parameters of the lexicographic product, J. Combin. Theory Ser. B 19 (1975) 87-95.
10. D. Greenwell and L. Lovász, Applications of product colouring, Acta Math. Acad. Sci. Hungar. 25 (1974) 335-340.
11. R. Häggkvist, P. Hell, D.J. Miller and V. Neumann Lara, On multiplicative graphs and the product conjecture, Combinatorica 8 (1988) 63-74.
12. 1-chromatic graphs can be countable, Combinatorica 5 (1985) 137-139.
13. G. Hajós, Über eine Konstruktion nicht n-färbbarer Graphen, Wiss. Z. Martin-Luther Univ. Halle-Wittenberg Math. Natur. Reihe 10 (1961) 116-117.
14. S. Hedetniemi, Homomorphisms of graphs and automata, Univ. Michigan, Technical Report 03105-44-T, 1966.
15. P. Hell and F. Roberts, Analogues of the Shannon capacity of a graph, Ann. Discrete Math. 12 (1982) 155-168.
16. W. Imrich and S. Klavžar, Retracts of strong products of graphs, Discrete Math. 109 (1992) 147-154.
17. P.K. Jha, Hypercubes, Median graphs and products of graphs: Some algorithmic and combinatorial results, Ph.D. Thesis, Iowa State Univ., 1990.
18. R. Kaschek and S. Klavžar, On the chromatic number of the lexicographic product of graphs, Indian J. Pure Appl. Math. 25 (1994) 1267-1274.
19. S. Klavžar, Two remarks on retracts of graph products, Discrete Math. 109 (1992) 155-160.
20. χ-critical graphs, Aequationes Math. 45 (1993) 153-162.
21. S. Klavžar and U. Milutinović, Strong products of Kneser graphs, Discrete Math. 133 (1994) 297-300.
22. N. Linial and U. Vazirani, Graph products and chromatic numbers, in: Proc. 30th Ann. IEEE Symp. on Foundations of Computer Science (1989) 124-128.
23. L. Lovász, Kneser's conjecture, chromatic number, and homotopy, J. Combin. Theory Ser. A 25 (1978) 319-324.
24. L. Lovász, Combinatorial Problems and Exercises (North-Holland, Amsterdam, 1979).
25. D.J. Miller, The categorical product of graphs, Canad. J. Math. 20 (1968) 1511-1521.
26. J. Nešetřil, Representations of graphs by means of products and their complexity, Lecture Notes in Computer Science 118 (1981) 94-102.
27. J. Nešetřil and V. Rödl, Products of graphs and their applicatons, Lecture Notes in Math. 1018 (1983) 151-160.
28. S. Poljak, Coloring digraphs by iterated antichains, Comment. Math. Univ. Carolin. 32 (1991) 209-212.
29. S. Poljak and V. Rödl, On the arc-chromatic number of a digraph, J. Combin. Theory Ser. B 2 (1981) 190-198.
30. V. Puš, Chromatic number of products of graphs, Comment. Math. Univ. Carolin. 29 (1988) 457-463.
31. G. Sabidussi, Graphs with given group and given graph-theoretical properties, Canad. J. Math. 9 (1957) 515-525.
32. N.W. Sauer and X. Zhu, Multiplicative posets, Order 8 (1992) 349-358.
33. N.W. Sauer and X. Zhu, An approach to Hedetniemi's conjecture, J. Graph Theory 16 (1992) 423-436.
34. A.A. Schäffer and A. Subramanian, A note on the chromatic number of the alternative negation of two graphs, Colloq. Math. 55 (1988) 367-370.
35. E. Sonnemann and O. Krafft, Independence numbers of product graphs, J. Combin. Theory Ser. B 17 (1974) 133-142.
36. L. Soukup, On chromatic number of product of graphs, Comment. Math. Univ. Carolin. 29 (1988) 1-12.
37. S. Stahl, n-tuple colorings and associated graphs, J. Combin. Theory Ser. B 20 (1976) 185-203.
38. D. Turzik, A note on chromatic number of direct product of graphs, Comment. Math. Univ. Carolin. 24 (1983) 461-463.
39. K. Vesztergombi, Some remarks on the chromatic number of the strong product of graphs, Acta Cybernet. 4 (1978/79) 207-212.
40. K. Vesztergombi, Chromatic number of strong product of graphs, Colloq. Math. Soc. János Bolyai 25 (1981) 819-825.
41. E. Weltz, Symmetric graphs and interpretations, J. Combin. Theory Ser. B 37 (1984) 235-244.
42. K.W. Yang, Chromatic number of cartesian sum of two graphs, Proc. Amer. Math. Soc. 19 (1968) 617-618.
43. H. Zhou, Multiplicativity. Part I. Variations, multiplicative graphs, and digraphs, J. Graph Theory 15 (1991) 469-488.
44. H. Zhou, Multiplicativity. Part II. Nonmultiplicative digraphs and characterization of oriented paths, J. Graph Theory 15 (1991) 489-509.
45. X. Zhu, personal communication.