A sharp threshold for random graphs with a monochromatic triangle in every edge coloring.0821838253 A sharp threshold for random graphs In mathematics, a random graph is a graph that is generated by some random process. The theory of random graphs lies at the intersection between graph theory and probability theory, and studies the properties of typical random graphs. with a monochromatic triangle The monochromatic triangle problem is a decision problem that is known to be NP-complete. Input: An n-node undirected graph G(V,E) with node set V and edge set E. in every edge coloring In graph theory, edge coloring is one type of the graph coloring problem. A coloring of a graph's edges assigns a "color" to each edge of the graph. The objective is to color the graph's edges so that no vertex has two edges leaving it that have the same "color" and to use as few . Ed. by Ehud Friedgut et al. Amer. Mathematical Society 2006 66 pages $50.00 Paperback Memoirs of the American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ; no.845 QA3 The authors propose the R is the set of all finite graphs G with the Ramsey property that every coloring of the edges of G by two colors yields a monochromatic triangle. In this paper they establish a sharp threshold for random graphs with this property. They examine the concept and its implications in full, determining that a crucial tool that is used in the proof and is of independent interest is a generalization of Szemeredi's regularity lemma lemma (lĕm`ə): see theorem. (logic) lemma - A result already proved, which is needed in the proof of some further result. to a certain hypergraph setting. They provide an outline of the proof, tepees and constellations, regularity, the core section (proof of Lemma 2.4), random graphs, a summary and a glossary. ([c]20072005 Book News, Inc., Portland, OR) |
|
||||||||||||||||
Printer friendly
Cite/link
Email
Feedback
Reader Opinion