On 2-cell imbeddings of complete n-partite graphs
On 2-factors in squares of graphs
On 2-periodic graphs of a certain graph operator
We deal with the graph operator defined to be the complement of the square of a graph: . 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 can be decomposed in two edge-disjoint factors from . We further show that all the incidence graphs of Desarguesian finite projective geometries...
On 2-ranks of Steiner triple systems.
On 3-harness weaving: cataloging designs generated by fundamental blocks having distinct rows and columns.
On 3-simplicial vertices in planar graphs
A vertex v in a graph G = (V,E) is k-simplicial if the neighborhood N(v) of v can be vertex-covered by k or fewer complete graphs. The main result of the paper states that a planar graph of order at least four has at least four 3-simplicial vertices of degree at most five. This result is a strengthening of the classical corollary of Euler's Formula that a planar graph of order at least four contains at least four vertices of degree at most five.
On -choosability of toroidal graphs without chordal 7-cycles and adjacent 4-cycles
A graph is called -choosable if for every list assignment satisfying for all , there is an -coloring of such that each vertex of has at most neighbors colored with the same color as itself. In this paper, it is proved that every toroidal graph without chordal 7-cycles and adjacent 4-cycles is -choosable.
On (4, 2)-digraphs containing a cycle of length 2.
On -connected, planar -almost pancyclic graphs
On a -factor of the fourth power of a connected graph
On a balanced property of derangements.
On a bound on algebraic connectivity: the case of equality
In a recent paper the authors proposed a lower bound on , where , , is an eigenvalue of a transition matrix of an ergodic Markov chain. The bound, which involved the group inverse of , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in the bound when...
On a certain analogy of Stirling's numbers of the 2nd kind
On a certain class of multidigraphs, for which reversal of no arc decreases the number of their cycles
On a certain class of polytopes associated with independence systems.
On a certain distance between isomorphism classes of graphs
On a certain homomorphism properties of graphs II.
On a certain numbering of the vertices of a hypergraph
On a certain ordering of the vertices of a tree
On a Certain Type of Decompositions of Complete Graphs into Factors with Equal Diameters