1 research outputs found
A Proof of the Erd\"os - Faber - Lov\'asz Conjecture
In 1972, Erd\"{o}s - Faber - Lov\'{a}sz (EFL) conjectured that, if
is a linear hypergraph consisting of edges of cardinality ,
then it is possible to color the vertices with colors so that no two
vertices with the same color are in the same edge. In 1978, Deza, Erd\"{o}s and
Frankl had given an equivalent version of the same for graphs: Let denote a graph with complete graphs , each having exactly vertices and have the property that every pair of
complete graphs has at most one common vertex, then the chromatic number of
is . The clique degree of a vertex in is given by . In this paper we give an algorithmic
proof of the conjecture using the symmetric latin squares and clique degrees of
the vertices of .Comment: 10 pages. arXiv admin note: substantial text overlap with
arXiv:1508.0347