For two graphs G and H, let the mixed anti-Ramsey numbers, maxR(n; G, H), (minR(n; G, H)) be the maximum (minimum) number of colors used in an edge-coloring of a complete graph wi...
For planar graphs, counting the number of perfect matchings (and hence determining whether there exists a perfect matching) can be done in NC [4, 10]. For planar bipartite graphs, ...
We prove that for fixed integer D and positive reals α and γ, there exists a constant C0 such that for all p satisfying p(n) ≥ C0/n, the random graph G(n, p) asymptotically a...
Gerards and Seymour (see [T.R. Jensen, B. Toft, Graph Coloring Problems, Wiley-Interscience, 1995], page 115) conjectured that if a graph has no odd complete minor of order p, the...
The Lov´asz theta number of a graph G can be viewed as a semidefinite programming relaxation of the stability number of G. It has recently been shown that a copositive strengthe...