论文标题
关于超图边缘着色问题的猜想
On a Conjecture for a Hypergraph Edge Coloring Problem
论文作者
论文摘要
令$ h =（\ MATHCAL {M} \ CUP \ MATHCAL {J}，E \ CUP \ MATHCAL {e}）$是两个超插图$ \ MATHCAL {G} _1 $和$ \ MATHCAL {g} _1 $和$ \ MATHCAL {g} _2 $ \ \ MATHCAL} \ Cup \ Mathcal {G} _ {2} $和$ \ Mathcal {G} _ {1} \ CAP \ MATHCAL {G} _ {2} = \ varnothing $。在Bi-Partite Multigraph Graph $（\ Mathcal {M} \ Cup \ Cup \ Mathcal {J}，E），E $中的边缘$ \ { \ Mathcal {e} $，$ \ ell = 1,2 $，具有整数乘以$ a_ {j \ ell} $。在[5]中已经推测，$χ\ prime（h）= \lceilχ\ prime _ {f}（h）\ rceil $，其中$χ\ prime（h）$和$χ\χ\ prime _ {f}（h）$是$ h $ $ h $ h $ h $和flactaction Edge Edge Edge Edge Edge Edge Edge Chromical Chromical Chromical chollomentical os $ h $的边缘。研究这种超越着色猜想的动机来自大学的时间表，以及与多处理器的开放式商店计划。我们在本文中证明了这个猜想。
Let $H =(\mathcal{M} \cup \mathcal{J} ,E \cup \mathcal{E})$ be a hypergraph with two hypervertices $\mathcal{G}_1$ and $\mathcal{G}_2$ where $\mathcal{M} =\mathcal{G}_{1} \cup \mathcal{G}_{2}$ and $\mathcal{G}_{1} \cap \mathcal{G}_{2} =\varnothing $. An edge $\{h ,j\} \in E$ in a bi-partite multigraph graph $(\mathcal{M} \cup \mathcal{J} ,E)$ has an integer multiplicity $b_{j h}$, and a hyperedge $\{\mathcal{G}_{\ell } ,j\} \in \mathcal{E}$, $\ell=1,2$, has an integer multiplicity $a_{j \ell }$. It has been conjectured in [5] that $χ\prime (H) =\lceil χ\prime _{f} (H)\rceil $, where $χ\prime (H)$ and $χ\prime _{f} (H)$ 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.
