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A fundamental result of Kuhn and Osthus [The minimum degree threshold for perfect graph packings, Combinatorica, 2009] determines up to an additive constant the minimum degree threshold that forces a graph to contain a perfect H-tiling. We prove a degree sequence version of this result which allows for a significant number of vertices to have lower degree.
We give the following extension of Baranys colorful Caratheodory theorem: Let M be an oriented matroid and N a matroid with rank function r, both defined on the same ground set V and satisfying rank(M) < rank(N). If every subset A of V with r(V - A)
Komlos [Komlos: Tiling Turan Theorems, Combinatorica, 2000] determined the asymptotically optimal minimum-degree condition for covering a given proportion of vertices of a host graph by vertex-disjoint copies of a fixed graph H, thus essentially exte
In two papers, Little and Sellers introduced an exciting new combinatorial method for proving partition identities which is not directly bijective. Instead, they consider various sets of weighted tilings of a $1 times infty$ board with squares and do
For a collection $mathbf{G}={G_1,dots, G_s}$ of not necessarily distinct graphs on the same vertex set $V$, a graph $H$ with vertices in $V$ is a $mathbf{G}$-transversal if there exists a bijection $phi:E(H)rightarrow [s]$ such that $ein E(G_{phi(e)}
Let G be a simple connected graph of order n with degree sequence d_1, d_2, ..., d_n in non-increasing order. The spectral radius rho(G) of G is the largest eigenvalue of its adjacency matrix. For each positive integer L at most n, we give a sharp up