Abstract
Let F be a finite family of sets and G(F) be the intersection graph of F (the vertices of G(F) are the sets of family F and the edges of G(F) correspond to intersecting pairs of sets). The transversal number τ(F) is the minimum number of points meeting all sets of F. The independent (stability) number α(F) is the maximum number of pairwise disjoint sets in F. The clique number ω(F) is the maximum number of pairwise intersecting sets in F. The coloring number q(F) is the minimum number of classes in a partition of F into pairwise disjoint sets.
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References
Gýarfás, A., Lehel, J.: Covering and coloring problems for relatives of intervals. Discrete Math. 55, 167–180 (1985)
Károlyi, G.: On point covers of parallel rectangles. Periodica Mathematica Hungarica 23(2), 105–107 (1991)
Fon-Der-Flaass, D.G., Kostochka, A.V.: Covering boxes by points. Discrete Math. 120, 269–275 (1993)
Asplund, E., Grünbaum, B.: On a coloring problem. Math. Scand. 8, 181–188 (1960)
Burling, J.: On coloring problems of families of prototypes, Ph.D. Thesis, University of Colorado Boulder, CO (1965)
Akiyama, J., Hosono, K., Urabe, H.: Some combinatorial problems. Discrete Math. 116, 291–298 (1993)
Perepelitsa, I.: The estimates of the chromatic number of the intersection graphs of figures on the plane (personal communication)
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Ahlswede, R., Karapetyan, I. (2006). Intersection Graphs of Rectangles and Segments. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_68
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DOI: https://doi.org/10.1007/11889342_68
Publisher Name: Springer, Berlin, Heidelberg
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