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Tytuł artykułu

The cost chromatic number and hypergraph parameters

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Języki publikacji
EN
Abstrakty
EN
In a graph, by definition, the weight of a (proper) coloring with positive integers is the sum of the colors. The chromatic sum is the minimum weight, taken over all the proper colorings. The minimum number of colors in a coloring of minimum weight is the cost chromatic number or strength of the graph. We derive general upper bounds for the strength, in terms of a new parameter of representations by edge intersections of hypergraphs.
Twórcy
  • Computer and Automation Institute, Hungarian Academy of Sciences, H-1111 Budapest, Kende u. 13-17, Hungary
autor
  • Computer and Automation Institute, Hungarian Academy of Sciences, H-1111 Budapest, Kende u. 13-17, Hungary
Bibliografia
  • [1] Y. Alavi, P. Erdős, P.J. Malde, A.J. Schwenk and C. Thomassen, Tight bounds on the chromatic sum of a connected graph, J. Graph Theory 13 (1989) 353-357, doi: 10.1002/jgt.3190130310.
  • [2] U. Feigle, L. Lovász and P. Tetali, Approximating sum set cover, Algorithmica 40 (2004) 219-234, doi: 10.1007/s00453-004-1110-5.
  • [3] M. Gionfriddo, F. Harary and Zs. Tuza, The color cost of a caterpillar, Discrete Math. 174 (1997) 125-130, doi: 10.1016/S0012-365X(96)00325-1.
  • [4] E. Kubicka, Constraints on the chromatic sequence for trees and graphs, Congr. Numer. 76 (1990) 219-230.
  • [5] E. Kubicka and A.J. Schwenk, An introduction to chromatic sums, in: Proc. ACM Computer Science Conference, Louisville (Kentucky) 1989, 39-45.
  • [6] J. Mitchem and P. Morriss, On the cost chromatic number of graphs, Discrete Math. 171 (1997) 201-211, doi: 10.1016/S0012-365X(96)00005-2.
  • [7] J. Mitchem, P. Morriss and E. Schmeichel, On the cost chromatic number of outerplanar, planar and line graphs, Discuss. Math. Graph Theory 17 (1997) 229-241, doi: 10.7151/dmgt.1050.
  • [8] M. Molloy and B. Reed, Graph Colouring and the Probabilistic Method (Springer, 2002).
  • [9] T. Szkaliczki, Routing with minimum wire length in the Dogleg-free Manhattan Model, SIAM Journal on Computing 29 (1999) 274-287, doi: 10.1137/S0097539796303123.
  • [10] Zs. Tuza, Contractions and minimal k-colorability, Graphs and Combinatorics 6 (1990) 51-59, doi: 10.1007/BF01787480.
  • [11] Zs. Tuza, Problems and results on graph and hypergraph colorings, Le Matematiche 45 (1990) 219-238.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1329
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