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Displaying similar documents to “Digraphs contractible onto * K 3 ”

The directed distance dimension of oriented graphs

Gary Chartrand, Michael Raines, Ping Zhang (2000)

Mathematica Bohemica

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For a vertex v of a connected oriented graph D and an ordered set W = { w 1 , w 2 , ⋯ , w k } of vertices of D , the (directed distance) representation of v with respect to W is the ordered k -tuple r ( v | W ) = ( d ( v , w 1 ) , d ( v , w 2 ) , ⋯ , d ( v , w k ) ) , where d ( v , w i ) is the directed distance from v to w i . The set W is a resolving set for D if every two distinct vertices of D have distinct representations. The minimum cardinality of a resolving set for D is the (directed distance) dimension dim ( D ) of D . The dimension of a connected oriented graph need not be defined. Those oriented...

Exact 2 -step domination in graphs

Gary Chartrand, Frank Harary, Moazzem Hossain, Kelly Schultz (1995)

Mathematica Bohemica

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For a vertex v in a graph G , the set N 2 ( v ) consists of those vertices of G whose distance from v is 2. If a graph G contains a set S of vertices such that the sets N 2 ( v ) , v ∈ S , form a partition of V ( G ) , then G is called a 2 -step domination graph. We describe 2 -step domination graphs possessing some prescribed property. In addition, all 2 -step domination paths and cycles are determined.

On 2 -extendability of generalized Petersen graphs

Nirmala B. Limaye, Mulupuri Shanthi C. Rao (1996)

Mathematica Bohemica

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Let G P ( n , k ) be a generalized Petersen graph with ( n , k ) = 1 , n > k ≥ 4 . Then every pair of parallel edges of G P ( n , k ) is contained in a 1-factor of G P ( n , k ) . This partially answers a question posed by Larry Cammack and Gerald Schrag [Problem 101, Discrete Math. 73(3), 1989, 311-312].

Symmetrized and continuous generalization of transversals

Martin Kochol (1996)

Mathematica Bohemica

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The theorem of Edmonds and Fulkerson states that the partial transversals of a finite family of sets form a matroid. The aim of this paper is to present a symmetrized and continuous generalization of this theorem.