Applications Of Lovász Local Lemma In Combinatorial Mathematics

Graph theory is an important part of Combinatorics.In this paper,we study the problem of high dimensional Ramsey number,r-uniform hypergraph and Adjacent ver-tex distinguishing total coloring.Paul Erdos and Noga Alon,who gives a general sense of Ramsey Number Theory.Joel Spencer prove asymptotic lower bound of Ramsey function by Lovász local lemma.Shan Chuanhui gives a general form Ramsey Number Theory of the dimensional case and generalized.This paper presents a another form Ramsey Number Theory of the dimensional case and generalized by Lovász local lem-ma.It includes the theory of high dimensional Ramsey number under the condition of equal probability and unequal probability.Lu Shanghui prove that the upper bound of the chromatic number of the adjacent vertex strong distinguishing total coloring is 32?by using the general form of the Lovász local lemma.In this paper,we give the upper bound on the chromatic number of adjacent vertex strong distinguishing total coloring of graph is 30? by using inference of Lovász local lemma.Lovász and Erdos give the conclusion that if each hypergraph edge and the other 2r-3 edges intersect at most,then there is a 2 vertex coloring,so that any edge is not monochromatic.This paper give its proof by using the general form of Lovász local lemma and extend it to the vertex k coloring.