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706  Articles
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In a graph, a cycle whose length is a power of two (that is, 2k) is called a 2-power cycle. In this paper, we show that the existence of an infinite family of cubic graphs which contain only one cycle whose length is a power of 2. Such graphs are cal... see more

Let H=(V,E)\mathcal{H}=(V,\mathcal{E}) be an rr-uniform hypergraph on nn vertices and fix a positive integer kk such that 1=k=r1\le k\le r. A kk-matching of H\mathcal{H} is a collection of edges M?E\mathcal{M}\subset \mathcal{E} such that every subset of ... 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

Turán-type problem is one of central problems in extremal graph theory. Erdos et al. [J. Combin. Theory Ser. B 64 (1995) 89-100] obtained the exact Turán number of the friendship graph FkF_k for n=50k2n\geq 50k^2, and characterized all its extremal graphs... see more

A vertex of a graph is bisimplicial if the set of its neighbors is the union of two cliques; a graph is quasi-line if   every vertex is bisimplicial.    A recent result of Chudnovsky and Seymour asserts that every non-empty even-hole-free g... see more

Let p\pi be a permutation of the set [n]={1,2,…,n}[n]=\{1,2,\dots, n\}. Two disjoint order-isomorphic subsequences of p\pi are called twins. How long twins are contained in every permutation? The well known Erdos-Szekeres theorem implies that there is alw... see more

Erdos conjectured in 1946 that every n-point set P in convex position in the plane contains a point that determines at least ?n/2? distinct distances to the other points of P. The best known lower bound due to Dumitrescu (2006) is 13n/36-O(1). In the pres... see more

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