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It is shown that the Hilbert series of the face ring of a clique complex (equivalently, flag complex) of a graph G is, up to a factor, just a specialization of SG (x, y), the subg...
A mixed hypergraph is a triple H = (X, C, D), where X is the vertex set, and each of C, D is a list of subsets of X. A strict k-coloring of H is a surjection c : X {1, . . . , k}...
Tao Jiang, Dhruv Mubayi, Zsolt Tuza, Vitaly I. Vol...
Given a graph on n vertices which is the union of two comparability graphs on the same vertex set, it always contains a clique or independent set of size n 1 3 . On the other hand...
One of the classical problems concerning the peg solitaire game is the feasibility issue. Tools used to show the infeasibility of various peg games include valid inequalities, know...
An orientation of a digraph D is a spanning subdigraph of D obtained from D by deleting exactly one arc between x and y for every pair x = y of vertices such that both xy and yx a...
Gregory Gutin, Khee Meng Koh, Eng Guan Tay, Anders...
We prove that for every c > 0 there exists a constant K = K(c) such that every graph G with n vertices and minimum degree at least cn contains a cycle of length t for every even...