The bipartite case of the Bollob as and Koml os conjecture states that for every 0; > 0 there is an = ( 0; ) > 0 such that the following statement holds: If G is any graph with (G) n2 + n; then Gâ€¦ (More)

We address the problem of connection preemption in a multi-class network environment. Our objective is: (i) to minimize the number of preempted connections, and (ii) to minimize the total preemptedâ€¦ (More)

Let G = (V, E) be an undirected graph and C(G) denote the set of all cycles in G. We introduce a graph invariant cycle discrepancy, which we define as cycdisc(G) = min Ï‡:V !â†’{+1,âˆ’1} max CâˆˆC(G) âˆ£âˆ£âˆ£âˆ£ âˆ‘â€¦ (More)

The star graph S n is a graph with S n the set of all permutations over f1; : : :; ng as its vertex set; two vertices 1 and 2 are connected if 1 can be obtained form 2 by swapping the rst element ofâ€¦ (More)

Let be a nite alphabet and x 2 n. A string y 2 m is said to be k-dissimilar to x, if no k length substring of x is equal to any k length substring of y. We present an O(n log n) algorithm which onâ€¦ (More)

A graph, G, is called uniquely Hamiltonian if it contains exactly one Hamilton cycle. We show that if G = (V , E) is uniquely Hamiltonian then âˆ‘ vâˆˆV ( 2 3 )d(v)âˆ’#(G) â‰¥ 1. Where #(G) = 1 if G has evenâ€¦ (More)