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Displaying 1 – 20 of 109

Odd cycles and a class of facets of the axial 3-index assignment polytope

R. Euler (1987)

Applicationes Mathematicae

On 2-periodic graphs of a certain graph operator

Ivan Havel, Bohdan Zelinka (2001)

Discussiones Mathematicae Graph Theory

We deal with the graph operator $\bar{P o w ₂}$ defined to be the complement of the square of a graph: $\bar{P o w ₂} (G) = \bar{P o w ₂ (G)}$ . Motivated by one of many open problems formulated in [6] we look for graphs that are 2-periodic with respect to this operator. We describe a class of bipartite graphs possessing the above mentioned property and prove that for any m,n ≥ 6, the complete bipartite graph $K_{m, n}$ can be decomposed in two edge-disjoint factors from . We further show that all the incidence graphs of Desarguesian finite projective geometries...

On $4$ -connected, planar $4$ -almost pancyclic graphs

Marián Trenkler (1989)

Mathematica Slovaca

On a certain class of multidigraphs, for which reversal of no arc decreases the number of their cycles

Jozef Jirásek (1987)

Commentationes Mathematicae Universitatis Carolinae

On a class of polynomially solvable travelling salesman problems

M. Michalski (1987)

Applicationes Mathematicae

On a class of polynomials associated with the paths in a graph and its application to minimum nodes disjoint path coverings of graphs.

Farrell, E.J. (1983)

International Journal of Mathematics and Mathematical Sciences

On a conjecture concerning the Petersen graph.

Nelson, Donald, Plummer, Michael D., Robertson, Neil, Zha, Xiaoya (2011)

The Electronic Journal of Combinatorics [electronic only]

On a discrete Dido-type question.

K. Bezdek, A. Bezdek (1989)

Elemente der Mathematik

On a Hamiltonian cycle of the fourth power of a connected graph

Elena Wisztová (1991)

Mathematica Bohemica

In this paper the following theorem is proved: Let $G$ be a connected graph of order $p \geq 4$ and let $M$ be a matching in $G$ . Then there exists a hamiltonian cycle $C$ of $G^{4}$ such that $E (C) ⋂ M = 0$ .

On a minimum cycle basis of a graph

E. Kolasińska (1980)

Applicationes Mathematicae

On a power of cyclically ordered sets

Vítězslav Novák, Miroslav Novotný (1984)

Časopis pro pěstování matematiky

On a problem of Marco Buratti.

Horak, Peter, Rosa, Alexander (2009)

The Electronic Journal of Combinatorics [electronic only]

On a problem of P. Vestergaard concerning circuits in graphs

Bohdan Zelinka (1987)

Czechoslovak Mathematical Journal

On a problem of R. Häggkvist concerning edge-colourings of graphs

Bohdan Zelinka (1978)

Časopis pro pěstování matematiky

On a problem of walks

Charles Delorme, Marie-Claude Heydemann (1999)

Annales de l'institut Fourier

In 1995, F. Jaeger and M.-C. Heydemann began to work on a conjecture on binary operations which are related to homomorphisms of De Bruijn digraphs. For this, they have considered the class of digraphs $G$ such that for any integer $k$ , $G$ has exactly $n$ walks of length $k$ , where $n$ is the order of $G$ . Recently, C. Delorme has obtained some results on the original conjecture. The aim of this paper is to recall the conjecture and to report where all the authors arrived.

On arbitrarily vertex decomposable unicyclic graphs with dominating cycle

Sylwia Cichacz, Irmina A. Zioło (2006)

Discussiones Mathematicae Graph Theory

A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n₁,...,nₖ) of positive integers such that $\sum_{i = 1}^{k} n_{i} = n$ , there exists a partition (V₁,...,Vₖ) of vertex set of G such that for every i ∈ 1,...,k the set $V_{i}$ induces a connected subgraph of G on $n_{i}$ vertices. We consider arbitrarily vertex decomposable unicyclic graphs with dominating cycle. We also characterize all such graphs with at most four hanging vertices such that exactly two of them have a common neighbour.

Currently displaying 1 – 20 of 109

Page 1 Next

Displaying 1 – 20 of 109

Odd cycles and a class of facets of the axial 3-index assignment polytope

On 2-periodic graphs of a certain graph operator

On $4$ -connected, planar $4$ -almost pancyclic graphs

On a certain class of multidigraphs, for which reversal of no arc decreases the number of their cycles

On a class of polynomially solvable travelling salesman problems

On a class of polynomials associated with the paths in a graph and its application to minimum nodes disjoint path coverings of graphs.

On a conjecture concerning the Petersen graph.

On a discrete Dido-type question.

On a Hamiltonian cycle of the fourth power of a connected graph

On a minimum cycle basis of a graph

On a power of cyclically ordered sets

On a problem of Marco Buratti.

On a problem of P. Vestergaard concerning circuits in graphs

On a problem of R. Häggkvist concerning edge-colourings of graphs

On a problem of walks

On arbitrarily vertex decomposable unicyclic graphs with dominating cycle

On certain extensions of intervals in graphs

On certain regular graphs of girth 5.

On coefficients of circuit polynomials and characteristic polynomials.

On coefficients of path polynomials.

Currently displaying 1 – 20 of 109