Quantum walk search on the complete bipartite graph

On Subgraphs of the Complete Bipartite Graph

G(n) denotes a graph of n vertices and G(n) denotes its complementary graph. In a complete graph every two distinct vertices are joined by an edge. Let C k (G(n)) denote the number of complete subgraphs of k vertices contained in G(n). Recently it was proved [1] that for every k 2 (n) (1) min C (G (n)) + Ck(G(n)) < k k, , ! 2 2 where the minimum is over all graphs G(n). It seems likely that (1)...

Explicit Bound on Cover Time and Cover Time of Random Walk on Complete Bipartite Graph

Cluttered orderings for the complete bipartite graph

To minimize the access cost in large disk arrays (RAID) Cohen et al. [5–7] introduced (d, f)-cluttered orderings of various set systems, d, f ∈ N. In case of a graph this amounts to an ordering of the edge set such that the number of points contained in any d consecutive edges is bounded by the number f . For the complete graph, Cohen et al. gave some optimal solution for small parameters d [5]...

On the parameter μ21 of a complete bipartite graph

A proper edge t-coloring of a graph G is a coloring of edges of G with colors 1, 2, ..., t such that all colors are used, and no two adjacent edges receive the same color. The set of colors of edges incident with a vertex x is called a spectrum of x. An arbitrary nonempty subset of consecutive integers is called an interval. Suppose that all edges of a graph G are colored in the game of Alice a...

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