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Abstrakty
Let τ(G) denote the number of vertices in a longest path of the graph G and let k₁ and k₂ be positive integers such that τ(G) = k₁ + k₂. The question at hand is whether the vertex set V(G) can be partitioned into two subsets V₁ and V₂ such that τ(G[V₁] ) ≤ k₁ and τ(G[V₂] ) ≤ k₂. We show that several classes of graphs have this partition property.
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
113-125
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-10-10
poprawiono
1998-02-27
Twórcy
autor
- Rand Afrikaans University, Auckland Park, 2006 South Africa
autor
- Rand Afrikaans University, Auckland Park, 2006 South Africa
autor
- Converse College, Spartanburg, SC 29302 USA
autor
- University of South Africa, Pretoria, 0001 South Africa
Bibliografia
- [1] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discussiones Mathematicae Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.
- [2] I. Broere, M. Frick and G. Semanišin, Maximal graphs with respect to hereditary properties, Discussiones Mathematicae Graph Theory 17 (1997) 51-66, doi: 10.7151/dmgt.1038.
- [3] I. Broere, P. Hajnal and P. Mihók, Partition problems and kernels of graph, Discussiones Mathematicae Graph Theory 17 (1997) 311-313, doi: 10.7151/dmgt.1058.
- [4] G. Chartrand, D.P. Geller and S.T. Hedetniemi, A generalization of the chromatic number, Proc. Camb. Phil. Soc. 64 (1968) 265-271, doi: 10.1017/S0305004100042808.
- [5] G. Chartrand and L. Lesniak, Graphs and Digraphs, second edition (Wadsworth & Brooks/Cole, Monterey, 1986).
- [6] G. Dirac, Some theorems on abstract graphs, Proc. London Math. Soc. 2 (1952) 69-81, doi: 10.1112/plms/s3-2.1.69.
- [7] P. Hajnal, Graph partitions (in Hungarian), Thesis, supervised by L. Lovász, J.A. University, Szeged, 1984.
- [8] L. Kászonyi and Zs. Tuza, Saturated graphs with minimal number of edges, J. Graph Theory 10 (1986) 203-210, doi: 10.1002/jgt.3190100209.
- [9] J.M. Laborde, C. Payan and N.H. Xuong, Independent sets and longest directed paths in digraphs, in: Graphs and other combinatorial topics (Prague, 1982), 173-177 (Teubner-Texte Math., 59, 1983).
- [10] L. Lovász, On decomposition of graphs, Studia Sci. Math. Hungar 1 (1966) 237-238.
- [11] P. Mihók, Problem 4, p. 86 in: M. Borowiecki and Z. Skupień (eds), Graphs, Hypergraphs and Matroids (Zielona Góra, 1985).
- [12] M. Stiebitz, Decomposing graphs under degree constraints, J. Graph Theory 23 (1996) 321-324, doi: 10.1002/(SICI)1097-0118(199611)23:3<321::AID-JGT12>3.0.CO;2-H
- [13] J. Vronka, Vertex sets of graphs with prescribed properties (in Slovak), Thesis, supervised by P. Mihók, P.J. Šafárik University, Košice, 1986.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1068