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- W2522730684 abstract "A decomposition of a simple graph $G$ is a pair $(G,P)$ where $P$ is a set of subgraphs of $G$, which partitions the edges of $G$ in the sense that every edge of $G$ belongs to exactly one subgraph in $P$. If the elements of $P$ are induced subgraphs then the decomposition is denoted by $[G,P]$. A $k$-$P$-coloring of a decomposition $(G,P)$ is a surjective function that assigns to the edges of $G$ a color from a $k$-set of colors, such that all edges of $Hin P$ have the same color, and, if $H_1,H_2in P$ with $V(H_1)cap V(H_2)neqemptyset$ then $E(H_1)$ and $E(H_2)$ have different colors. The emph{chromatic index} $chi'((G,P))$ of a decomposition $(G,P)$ is the smallest number $k$ for which there exists a $k$-$P$-coloring of $(G,P)$. The well-known Erdos-Faber-Lov'asz Conjecture states that any decomposition $[K_n,P]$ satisfies $chi'([K_n,P])leq n$. We use quasigroups and complete digraphs to give a new family of decompositions that satisfy the conjecture." @default.
- W2522730684 created "2016-09-30" @default.
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- W2522730684 date "2015-08-22" @default.
- W2522730684 modified "2023-09-27" @default.
- W2522730684 title "A note on the Erdos-Faber-Lov'asz Conjecture: quasigroups and complete digraphs" @default.
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