On coverings of random graphs
On covers of abelian groups by cosets
On critical and cocritical radius edge-invariant graphs
The concepts of critical and cocritical radius edge-invariant graphs are introduced. We prove that every graph can be embedded as an induced subgraph of a critical or cocritical radius-edge-invariant graph. We show that every cocritical radius-edge-invariant graph of radius r ≥ 15 must have at least 3r+2 vertices.
On cross-intersecting uniform sub-families of hereditary families.
On cubes and dichotomic trees
On cubic planar hypohamiltonian and hypotraceable graphs.
On cycles in the coprime graph of integers.
On Cycles in Tournaments
On cyclically embeddable graphs
An embedding of a simple graph G into its complement G̅ is a permutation σ on V(G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider some families of embeddable graphs such that the corresponding permutation is cyclic.
On cyclically embeddable (n,n)-graphs
An embedding of a simple graph G into its complement G̅ is a permutation σ on V(G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider the embeddable (n,n)-graphs. We prove that with few exceptions the corresponding permutation may be chosen as cyclic one.
On -algebras
On Davis-Januszkiewicz homotopy types I: formality and rationalisation.
On Decomposing Regular Graphs Into Isomorphic Double-Stars
A double-star is a tree with exactly two vertices of degree greater than 1. If T is a double-star where the two vertices of degree greater than one have degrees k1+1 and k2+1, then T is denoted by Sk1,k2 . In this note, we show that every double-star with n edges decomposes every 2n-regular graph. We also show that the double-star Sk,k−1 decomposes every 2k-regular graph that contains a perfect matching.
On Decompositions of Complete Graphs into Factors with Given Radii
On decompositions of complete graphs into factors with given diameters and radii
On decompositions of complete graphs into three factors with given diameters
On decompositions of complete -uniform hypergraphs
On degree sequences of graphs with given cyclomatic number.
On degree sets and the minimum orders in bipartite graphs
For any simple graph G, let D(G) denote the degree set {degG(v) : v ∈ V (G)}. Let S be a finite, nonempty set of positive integers. In this paper, we first determine the families of graphs G which are unicyclic, bipartite satisfying D(G) = S, and further obtain the graphs of minimum orders in such families. More general, for a given pair (S, T) of finite, nonempty sets of positive integers of the same cardinality, it is shown that there exists a bipartite graph B(X, Y ) such that D(X) = S, D(Y )...
On degrees in the hasse diagram of the strong Bruhat order.