Rainbow matching in edge-colored graphs.
Rainbow numbers for small stars with one edge added
A subgraph of an edge-colored graph is rainbow if all of its edges have different colors. For a graph H and a positive integer n, the anti-Ramsey number f(n,H) is the maximum number of colors in an edge-coloring of Kₙ with no rainbow copy of H. The rainbow number rb(n,H) is the minimum number of colors such that any edge-coloring of Kₙ with rb(n,H) number of colors contains a rainbow copy of H. Certainly rb(n,H) = f(n,H) + 1. Anti-Ramsey numbers were introduced by Erdös et al. [5] and studied in...
Rainbow paths with prescribed ends.
Rainbow Tetrahedra in Cayley Graphs
Let Γn be the complete undirected Cayley graph of the odd cyclic group Zn. Connected graphs whose vertices are rainbow tetrahedra in Γn are studied, with any two such vertices adjacent if and only if they share (as tetrahedra) precisely two distinct triangles. This yields graphs G of largest degree 6, asymptotic diameter |V (G)|1/3 and almost all vertices with degree: (a) 6 in G; (b) 4 in exactly six connected subgraphs of the (3, 6, 3, 6)-semi- regular tessellation; and (c) 3 in exactly four connected...
Ramanujan grammar and Cayley trees. (Grammaire de Ramanujan et arbres de Cayley.)
Ramified Sets Of Pseudotrees
Ramified sets or pseudotrees.
Ramsey -minimal graphs.
Ramsey numbers for trees II
Let be the Ramsey number of the two graphs and . For let be the double star given by , and . We determine
Ramsey theorem for classes of hypergraphs with forbidden complete subhypergraphs
Ramsey theory applications.
Ramseyan properties of graphs.
Ramsey-type theorems
Random Cayley graphs are expanders: a simple proof of the Alon-Roichman theorem.
Random directed trees and forest -- drainage networks with dependence.
Random even graphs.
Random mappings, forests, and subsets associated with Abel-Cayley-Hurwitz multinomial expansions.
Random networks with sublinear preferential attachment: degree evolutions.
Random orderings and unique ergodicity of automorphism groups
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner andWeiss’s example of the group of all permutations...
Random Packings and Coverings in Random Trees