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1997 | 17 | 1 | 95-102
Tytuł artykułu

Partitions of some planar graphs into two linear forests

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A linear forest is a forest in which every component is a path. It is known that the set of vertices V(G) of any outerplanar graph G can be partitioned into two disjoint subsets V₁,V₂ such that induced subgraphs ⟨V₁⟩ and ⟨V₂⟩ are linear forests (we say G has an (LF, LF)-partition). In this paper, we present an extension of the above result to the class of planar graphs with a given number of internal vertices (i.e., vertices that do not belong to the external face at a certain fixed embedding of the graph G in the plane). We prove that there exists an (LF, LF)-partition for any plane graph G when certain conditions on the degree of the internal vertices and their neighbourhoods are satisfied.
Słowa kluczowe
Wydawca
Rocznik
Tom
17
Numer
1
Strony
95-102
Opis fizyczny
Daty
wydano
1997
otrzymano
1997-01-03
poprawiono
1997-02-25
Twórcy
  • Institute of Mathematics, Technical University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland
  • Institute of Mathematics, Technical University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland
Bibliografia
  • [1] M. Borowiecki, P. Mihók, Hereditary properties of graphs, in: Advances in Graph Theory (Vishwa International Publications, 1991) 41-68.
  • [2] P. Borowiecki, P-Bipartitions of Graphs, Vishwa International J. GraphTheory 2 (1993) 109-116.
  • [3] I. Broere, C.M. Mynhardt, Generalized colourings of outerplanar and planar graphs, in: Graph Theory with Applications to Algorithms and Computer Science (Wiley, New York, 1985) 151-161.
  • [4] W. Goddard, Acyclic colourings of planar graphs, Discrete Math. 91 (1991) 91-94, doi: 10.1016/0012-365X(91)90166-Y.
  • [5] T.R. Jensen and B. Toft, Graph Colouring Problems (Wiley-Interscience Publications, New York, 1995).
  • [6] P. Mihók, On the vertex partition numbers, in: M. Fiedler, ed., Graphs and Other Combinatorial Topics, Proc. Third Czech. Symp. Graph Theory, Prague, 1982 (Teubner-Verlag, Leipzig, 1983) 183-188.
  • [7] K.S. Poh, On the Linear Vertex-Arboricity of a Planar Graph, J. Graph Theory 14 (1990) 73-75, doi: 10.1002/jgt.3190140108.
  • [8] J. Wang, On point-linear arboricity of planar graphs, Discrete Math. 72 (1988) 381-384, doi: 10.1016/0012-365X(88)90229-4.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1042
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