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16.154  Articles
1 of 1.616 pages  |  10  records  |  more records»
One of the most important Turán’s theorems establishes an inequality between the maximum clique and the number of edges of a graph. Since 1941, this result has received much attention and many of the different proofs involve induction and a probability di... see more

Let G be a simple graph with n vertices, m edges and having adjacency eigenvalues ?1, ?2, …, ?n. The energy E(G) of the graph G is defined as E(G) = ?i = 1n|?i|. In this paper, we obtain the upper bounds for the energy E(G) in terms of the vertex covering... see more

Let kKr+1kK_{r+1} be the graph consisting of kk vertex-disjoint copies of the complete graph Kr+1K_{r+1}. Moon [Canad. J. Math. 20 (1968) 95--102] and Simonovits [Theory of Graphs (Proc. colloq., Tihany, 1996)] independently showed that if nn is sufficien... see more

For a graph GG, let cp(G)cp(G) denote the minimum number of cliques of GG needed to cover the edges of GG exactly once. Similarly, let bpk(G)bp_k(G) denote the minimum number of bicliques (i.e. complete bipartite subgraphs of GG) needed to cover each edge... see more

For a graph GG, let cp(G)cp(G) denote the minimum number of cliques of GG needed to cover the edges of GG exactly once. Similarly, let bpk(G)bp_k(G) denote the minimum number of bicliques (i.e. complete bipartite subgraphs of GG) needed to cover each edge... see more

A hole in a graph GG is an induced cycle of length at least four, and an even hole is a hole of even length. The diamond is the graph obtained from the complete graph K4K_4 by removing an edge. A pyramid is a graph consisting of a vertex aa called the&nbs... see more

Half graphs and their variants, such as semi-ladders and co-matchings, are configurations that encode total orders in graphs. Works by Adler and Adler (Eur. J. Comb.; 2014) and Fabianski et al. (STACS; 2019) prove that in powers of sparse graphs, one cann... see more

Let k=2k\ge 2 and n1=n2=n3=n4n_1\ge n_2\ge n_3\ge n_4 be integers such that n4n_4 is sufficiently larger than kk. We determine the maximum number of edges of a 4-partite graph with parts of sizes n1,…,n4n_1,\dots, n_4 that does not contain kk vertex-... see more

We prove that a family of pseudo-Paley graphs of square order obtained from unions of cyclotomic classes satisfies the Erdos-Ko-Rado (EKR) module property, in a sense that the characteristic vector of each maximum clique is a linear combination of charact... see more

1 of 1.616 pages  |  10  records  |  more records»