Further results on Erd?s Faber Lov sz conjecture

Abstract

In 1972, Erd?s Faber Lov sz (EFL) conjectured that, if H is a linear hypergraph consisting of n edges of cardinality n, then it is possible to color the vertices with n colors so that no two vertices with the same color are in the same edge. In 1978, Deza, Erd s and Frankl had given an equivalent version of the same for graphs: Let G=? i=1 n A i denote a graph with n complete graphs A 1 ,A 2 , ,A n , each having exactly n vertices and have the property that every pair of complete graphs has at most one common vertex, then the chromatic number of G is n. The clique degree d K (v) of a vertex v in G is given by d K (v)=|{A i :v?V(A i ),1?i?n}|. In this paper we give a method for assigning colors to the graphs satisfying the hypothesis of the Erd?s Faber Lov sz conjecture and every A i (1?i?n) has atmost [Formula presented] vertices of clique degree greater than one using Symmetric latin Squares and clique degrees of the vertices of G. 2019 Kalasalingam University