美国西弗吉尼亚大学Prof. Lai Hong-Jian校级学术报告(运筹学讨论班)

题目: Nowhere zero 3-flows and mod ($2p+1$)-orientations in graphs
报告人：Prof. Lai Hong-Jian （美国西弗吉尼亚大学）
时 间：5月16日 15：00-16：30
地 点：理科大楼A 1510
Abstract: We shall present a brief summary of this subject, with a concentration on some of the recent results we have done towards the 3-flow conjecture and the circular-flow conjecture. In particular, we obtained a sufficient and necessary condition for a graph to have an orientation with a preassigned out-degree at each vertex.This is then applied to show that every $(2p+1)log_2(|V(G)|)$-edge-connected graph $G$ has a mod $(2p+1)$-orientation. When $p=1$, this implies that every $3
log_2(|V(G)|)$-edge-connected graph $G$ has a nowhere zero 3-flow. We also established an equivalence between the contractible graphs with respect to the mod $(2p+1)$-orientability and the graphs with $K_{1, 2p+1}$-decompositions. This result is applied to disprove a conjecture proposed by Barat and Thomassen that every
4-edge-connected planar graph $G$ with $|V(G) equiv 0$ (mod 3) has a claw-decomposition. Further more, we proved a correct version of this Barat and Thomassen conjecture by showing that every 5-edge-connected planar graph $G$ with $|V(G) equiv 0$ (mod 3) has a claw-decomposition.

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数学系