- Publication venue
- Publication date
- 11/06/2020
- Field of study
Let H=(MβͺJ,EβͺE) be a hypergraph
with two hypervertices G1β and G2β where M=G1ββͺG2β and G1ββ©G2β=β
. An edge {h,j}βE in a bi-partite
multigraph graph (MβͺJ,E) has an integer
multiplicity bjhβ, and a hyperedge {Gββ,j}βE, β=1,2, has an integer multiplicity ajββ. It has
been conjectured in [5] that Οβ²(H)=βΟβ²fβ(H)β, where Οβ²(H) and Οβ²fβ(H) are the edge
chromatic number of H and the fractional edge chromatic number of H
respectively. Motivation to study this hyperedge coloring conjecture comes from
the University timetabling, and open shop scheduling with multiprocessors. We
prove this conjecture in this paper