We prove the following inequality: for every positive integer n and every collection X1, . . . , Xn of nonnegative independent random variables that each has expectation 1, the pr...
In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n ≥ 1, k ≥ 3, c ≥ 0 and G be an n-connected graph. Suppose that for eve...
For every real p > 0 and simple graph G, set f (p, G) = uV (G) dp (u) , and let (r, p, n) be the maximum of f (p, G) taken over all Kr+1-free graphs G of order n. We prove tha...
Let H be a multigraph and G a graph containing a subgraph isomorphic to a subdivision of H, with S ⊂ V (G) (the ground set) the image of V (H) under the isomorphism. We consider...
We consider graphs such as the minimum spanning tree, minimum Steiner tree, minimum matching, and traveling salesman tour for n points in the d-dimensional unit cube. For each of ...