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3.004  Articles
1 of 301 pages  |  10  records  |  more records»
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

A classical result of Erdos and Gallai determines the maximum size m(n,?)m(n,\nu) of a graph GG of order nn and matching number ?n\nu n. We show that GG has factorially many maximum matchings provided that its size is sufficiently close to m(n,?)m(n,\nu).

A conjecture by Aharoni and Berger states that every family of nn matchings of size n+1n+1 in a bipartite multigraph contains a rainbow matching of size nn. In this paper we prove that matching sizes of (32+o(1))n\left(\frac 3 2 + o(1)\right) n suffice to... see more

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

A classical result of Erdos and Gallai determines the maximum size m(n,?)m(n,\nu) of a graph GG of order nn and matching number ?n\nu n. We show that GG has factorially many maximum matchings provided that its size is sufficiently close to m(n,?)m(n,\nu).

We show that the bistatistic of right nestings and right crossings in matchings without left nestings is equidistributed with the number of occurrences of two certain patterns in permutations, and furthermore that this equidistribution holds when refined ... see more

A Hamiltonian graph is 2-factor Hamiltonian (2FH) if each of its 2-factors is a Hamiltonian cycle. A similar, but weaker, property is the Perfect-Matching-Hamiltonian property (PMH-property): a graph admitting a perfect matching is said to have this prope... see more

We study the relationship between two notions of pattern avoidance for involutions in the symmetric group and their restriction to fixed-point-free involutions. The first is classical, while the second appears in the geometry of certain spherical varietie... 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

1 of 301 pages  |  10  records  |  more records»