Old and new generalizations of line graphs.
On -factors in the cube of a graph
On a -factor of the fourth power of a connected graph
On a classification of Hamiltonian tournaments
On a conjecture of quintas and arc-traceability in upset tournaments
A digraph D = (V,A) is arc-traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V, i.e., hamiltonian path. We prove a conjecture of Quintas [7]: if D is arc-traceable, then the condensation of D is a directed path. We show that the converse of this conjecture is false by providing an example of an upset tournament which is not arc-traceable. We then give a characterization for upset tournaments in terms of their score sequences, characterize which arcs of...
On a family of cubic graphs containing the flower snarks
We consider cubic graphs formed with k ≥ 2 disjoint claws (0 ≤ i ≤ k-1) such that for every integer i modulo k the three vertices of degree 1 of are joined to the three vertices of degree 1 of and joined to the three vertices of degree 1 of . Denote by the vertex of degree 3 of and by T the set . In such a way we construct three distinct graphs, namely FS(1,k), FS(2,k) and FS(3,k). The graph FS(j,k) (j ∈ 1,2,3) is the graph where the set of vertices induce j cycles (note that the graphs...
On a Hamiltonian cycle of the fourth power of a connected graph
In this paper the following theorem is proved: Let be a connected graph of order and let be a matching in . Then there exists a hamiltonian cycle of such that .
On a problem of Marco Buratti.
On a problem of R. Häggkvist concerning edge-colourings of graphs
On balancing of hypergraphs
On Complex Eigenvalues of M and P Matrices.
On cubic planar hypohamiltonian and hypotraceable graphs.
On eulerian irregularity in graphs
A closed walk in a connected graph G that contains every edge of G exactly once is an Eulerian circuit. A graph is Eulerian if it contains an Eulerian circuit. It is well known that a connected graph G is Eulerian if and only if every vertex of G is even. An Eulerian walk in a connected graph G is a closed walk that contains every edge of G at least once, while an irregular Eulerian walk in G is an Eulerian walk that encounters no two edges of G the same number of times. The minimum length of an...
On eulerian subgraphs of complementary graphs
On -closed graphs
On Hamiltonian circuits and spanning trees of hypercubes
On Hamiltonian consecutive-d digraphs
On Hamiltonian cycles in two-triangle graphs
On Hamiltonian cycles of complete -partite graphs
On hypergraphs of maximal simple paths of a class of Hamiltonian graphs