On rainbow trees and cycles.
On rainbowness of semiregular polyhedra
We introduce the rainbowness of a polyhedron as the minimum number such that any colouring of vertices of the polyhedron using at least colours involves a face all vertices of which have different colours. We determine the rainbowness of Platonic solids, prisms, antiprisms and ten Archimedean solids. For the remaining three Archimedean solids this parameter is estimated.
On Ramsey graphs without cycles of short odd lengths
On Ramsey -minimal graphs
For graphs F, G and H, we write F → (G,H) to mean that any red-blue coloring of the edges of F contains a red copy of G or a blue copy of H. The graph F is Ramsey (G,H)-minimal if F → (G,H) but F* ↛ (G,H) for any proper subgraph F* ⊂ F. We present an infinite family of Ramsey -minimal graphs of any diameter ≥ 4.
On Ramsey minimal graphs.
On random greedy triangle packing.
On randomly colouring locally sparse graphs.
On randomly generated intersecting hypergraphs.
On randomly generated non-trivially intersecting hypergraphs.
On Randomly Hamiltonian Graphs.
On rank 2 geometries of the Mathieu group .
On rational radii coin representations of the wheel graph
A flower is a coin graph representation of the wheel graph. A petal of a flower is an outer coin connected to the center coin. The results of this paper are twofold. First we derive a parametrization of all the rational (and hence integer) radii coins of the 3-petal flower, also known as Apollonian circles or Soddy circles. Secondly we consider a general n-petal flower and show there is a unique irreducible polynomial Pₙ in n variables over the rationals ℚ, the affine variety of which contains the...
On recognition of strong graph bundles
On reconstructing of infinite forests
On recursively directed hypercubes.
On regular bipartite-preserving supergraphs.
On Regular Bipartite-Preserving Supergraphs. (Short Communication).
On regular factors in regular graphs with small radius.
ON RELATION BETWEEN SPECTRA OF GRAPHS AND THEIR DIGRAPH DECOMPOSITIONS
On relatively prime sets.