It is shown in this note that with high probability it is enough to destroy all triangles in order to get a cover graph from a random graph Gn,p with p log n/n for any constant ...
We provide a much shorter proof of the following partition theorem of P. Erdos and R. Rado: If X is an uncountable linear order into which neither 1 nor 1 embeds, then X (, 4)3 f...
Abstract. We introduce color-signed permutations to obtain a very explicit combinatorial interpretation of the q-Eulerian identities of Brenti and some generalizations. In particul...
Consider a connected r-regular n-vertex graph G with random independent edge lengths, each uniformly distributed on [0, 1]. Let mst(G) be the expected length of a minimum spanning...
The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of oth...