TY - JOUR

T1 - On the construction of non- 2 -colorable uniform hypergraphs

AU - Mathews, Jithin

AU - Panda, Manas Kumar

AU - Shannigrahi, Saswata

PY - 2015/1/10

Y1 - 2015/1/10

N2 - The problem of 2-coloring uniform hypergraphs has been extensively studied over the last few decades. An n-uniform hypergraph is not 2-colorable if its vertices cannot be colored with two colors, Red and Blue, such that every hyperedge contains Red as well as Blue vertices. The least possible number of hyperedges in an n-uniform hypergraph which is not 2-colorable is denoted by m(n). In this paper, we consider the problem of finding an upper bound on m(n) for small values of n. We provide constructions which improve the existing results for some such values of n. We obtain the first improvement in the case of n=8.

AB - The problem of 2-coloring uniform hypergraphs has been extensively studied over the last few decades. An n-uniform hypergraph is not 2-colorable if its vertices cannot be colored with two colors, Red and Blue, such that every hyperedge contains Red as well as Blue vertices. The least possible number of hyperedges in an n-uniform hypergraph which is not 2-colorable is denoted by m(n). In this paper, we consider the problem of finding an upper bound on m(n) for small values of n. We provide constructions which improve the existing results for some such values of n. We obtain the first improvement in the case of n=8.

KW - Hypergraph coloring

KW - Property B

KW - Uniform hypergraph

UR - http://www.scopus.com/inward/record.url?scp=85028151712&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2014.08.011

DO - 10.1016/j.dam.2014.08.011

M3 - Article

AN - SCOPUS:85028151712

VL - 180

SP - 181

EP - 187

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -