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This is a supplement for Pearls in graph theory -- a textbook written by Nora Hartsfield and Gerhard Ringel. Probabilistic method, Deletion-contraction formulas, Matrix theorem, Graph-polynomials, Generating functions, Minimum spanning trees, Marriage theorem and its relatives, Toroidal graphs, Rado graph.
This book is based on Graph Theory courses taught by P.A. Petrosyan, V.V. Mkrtchyan and R.R. Kamalian at Yerevan State University.
In this note we study graphs $G_r$ with the property that every colouring of $E(G_r)$ with $r+1$ colours admits a copy of some graph $H$ using at most $r$ colours. For $1le rle e(H)$ such graphs occur naturally at intermediate steps in the synthesis
The study of intersection problems in Extremal Combinatorics dates back perhaps to 1938, when Paul ErdH{o}s, Chao Ko and Richard Rado proved the (first) `ErdH{o}s-Ko-Rado theorem on the maximum possible size of an intersecting family of $k$-element s
We survey the published work of Harry Kesten in probability theory, with emphasis on his contributions to random walks, branching processes, percolation, and related topics. A complete bibliography is included of his publications.
Our goal is to present the basic results on one-dimensional Gibbs and equilibrium states viewed as special invariant measures on symbolic dynamical systems, and then to describe without technicalities a sample of results they allowed to obtain for ce