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2013 | 33 | 1 | 231-242
Tytuł artykułu

Choice-Perfect Graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Given a graph G = (V,E) and a set Lv of admissible colors for each vertex v ∈ V (termed the list at v), a list coloring of G is a (proper) vertex coloring ϕ : V → S v2V Lv such that ϕ(v) ∈ Lv for all v ∈ V and ϕ(u) 6= ϕ(v) for all uv ∈ E. If such a ϕ exists, G is said to be list colorable. The choice number of G is the smallest natural number k for which G is list colorable whenever each list contains at least k colors. In this note we initiate the study of graphs in which the choice number equals the clique number or the chromatic number in every induced subgraph. We call them choice-ω-perfect and choice-χ-perfect graphs, respectively. The main result of the paper states that the square of every cycle is choice-χ-perfect.
Słowa kluczowe
Wydawca
Rocznik
Tom
33
Numer
1
Strony
231-242
Opis fizyczny
Daty
wydano
2013-03-01
online
2013-04-13
Twórcy
autor
  • Alfréd Rényi Institute of Mathematics Hungarian Academy of Sciences H–1053 Budapest, Reáltanoda u. 13–15, Hungary, tuza@dcs.uni-pannon.hu
  • Department of Computer Science and Systems Technology University of Pannonia H–8200 Veszprém, Egyetem u. 10, Hungary
Bibliografia
  • [1] N. Alon and M. Tarsi, Colorings and orientations of graphs, Combinatorica 12 (1992) 125-134. doi:10.1007/BF01204715[Crossref]
  • [2] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50. doi:10.7151/dmgt.1037[Crossref]
  • [3] M. Borowiecki, E. Sidorowicz and Zs. Tuza, Game list colouring of graphs, Electron. J. Combin. 14 (2007) #R26.
  • [4] P. Erdős, A.L. Rubin and H. Taylor, Choosability in graphs, West-Coast Conference on Combinatorics, Graph Theory and Computing, Arcata, California, Congr. Numer. XXVI (1979) 125-157.
  • [5] H. Fleischner and M. Stiebitz, A solution to a colouring problem of P. Erdős, Discrete Math. 101 (1992) 39-48. doi:10.1016/0012-365X(92)90588-7[Crossref]
  • [6] F. Galvin, The list chromatic index of a bipartite multigraph, J. Combin. Theory (B) 63 (1995) 153-158. doi:10.1006/jctb.1995.1011[Crossref]
  • [7] S. Gravier and F. Maffray, Graphs whose choice number is equal to their chromatic number, J. Graph Theory 27 (1998) 87-97. doi:10.1002/(SICI)1097-0118(199802)27:2h87::AID-JGT4i3.0.CO;2-B[Crossref]
  • [8] S. Gravier and F. Maffray, On the choice number of claw-free perfect graphs, Discrete Math. 276 (2004) 211-218. doi:10.1016/S0012-365X(03)00292-9[Crossref]
  • [9] A.J.W. Hilton and P.D. Johnson, Jr., Extending Hall’s theorem, in: Topics in Combinatorics and Graph Theory-Essays in Honour of Gerhard Ringel (R. Bodendiek et al., Eds.), (Teubner, 1990) 359-371.
  • [10] A.J.W. Hilton and P.D. Johnson, Jr., The Hall number, the Hall index, and the total Hall number of a graph, Discrete Appl. Math. 94 (1999) 227-245. doi:10.1016/S0166-218X(99)00023-2[Crossref]
  • [11] M. Juvan, B. Mohar and R. ˇSkrekovski, List total colourings of graphs, Combin. Probab. Comput. 7 (1998) 181-188. doi:10.1017/S0963548397003210[Crossref]
  • [12] M. Juvan, B. Mohar and R. Thomas, List edge-colorings of series-parallel graphs, Electron. J. Combin. 6 (1999) #R42.
  • [13] D. Peterson and D.R. Woodall, Edge-choosability in line-perfect multigraphs, Discrete Math. 202 (1999) 191-199. doi:10.1016/S0012-365X(98)00293-3[Crossref]
  • [14] Zs. Tuza, Graph colorings with local constraints-A survey, Discuss. Math. Graph Theory 17 (1997) 161-228. doi:10.7151/dmgt.1049[Crossref]
  • [15] Zs. Tuza, Choice-perfect graphs and Hall numbers, manuscript, 1997.
  • [16] Zs. Tuza, Extremal jumps of the Hall number, Electron. Notes Discrete Math. 28 (2007) 83-89. doi:10.1016/j.endm.2007.01.012[Crossref]
  • [17] Zs. Tuza, Hall number for list colorings of graphs: Extremal results, Discrete Math. 310 (2010) 461-470. doi:10.1016/j.disc.2009.03.025[WoS][Crossref]
  • [18] Zs. Tuza and M. Voigt, List colorings and reducibility, Discrete Appl. Math. 79 (1997) 247-256. doi:10.1016/S0166-218X(97)00046-2[Crossref]
  • [19] V.G. Vizing, Coloring the vertices of a graph in prescribed colors, Metody Diskret. Anal. v Teorii Kodov i Schem 29 (1976) 3-10 (in Russian).
  • [20] D.R. Woodall, Edge-choosability of multicircuits, Discrete Math. 202 (1999) 271-277. doi:10.1016/S0012-365X(98)00297-0[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1660
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