A path(ological) partition problem

• Autorzy: Izak Broere , Michael Dorfling , Jean E. Dunbar , Marietjie Frick
• Języki publikacji: EN

Abstrakty

EN

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

EN

vertex partition; τ-partitionable; decomposable graph

Kategorie tematyczne

• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1998
• Tom: 18
• Numer: 1
• Strony: 113-125

Daty

wydano

1998

otrzymano

1997-10-10

poprawiono

1998-02-27

Twórcy

autor

Izak Broere

• Rand Afrikaans University, Auckland Park, 2006 South Africa

autor

Michael Dorfling

• Rand Afrikaans University, Auckland Park, 2006 South Africa

autor

Jean E. Dunbar

• Converse College, Spartanburg, SC 29302 USA

autor

Marietjie Frick

• University of South Africa, Pretoria, 0001 South Africa

Bibliografia

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• [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.
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Identyfikatory

DOI

10.7151/dmgt.1068