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來源:數學科研研究生作者:時間:2021-01-05瀏覽:10設置

報 告 人:范更華 传授

報告題目Circuit Covers in Signed Graphs

報告時間:2021年1月8日下午3:30

報告地點:9#1508

主辦單位:數學與統計學院、科學技術研究院

報告人簡介

范更華,福州大年夜學传授、博士生導師、曾任福州大年夜學副校長和全國組合數學與圖論學會理事長,現任離散數學及其應用教导部重點實驗室主任,1998年獲國家出色青年科學基金,2003年獲教导部科技一等獎,2005年獲國家天然科學二等獎獲。掌管多項國家天然科學基金重點項目與國家973計劃課題。重要從事圖論領域中的結構圖論、極圖理論、帶權圖、歐拉圖、整數流理論、子圖覆蓋等偏向的基礎理論研究。他的成果以“范定理”、“范條件”被國內外同业廣泛援用。一些成果還作為定理出現在國外出版的教科書中。擔任國際圖論界權威刊物《Journal of  Graph Theory》執行編委。

報告摘要

A signed graph is a graph G associated with a mapping . A signed circuit in a signed graph is a subgraph whose edges form a minimal dependent set in the signed graphic matroid. A signed graph is coverable if each edge is contained in some signed circuit. An oriented signed graph (bidirected graph) has a

nowhere-zero integer °ow if and only if it is coverable. A circuit-cover (circuit k-cover) of a signed graph G is a collection of signed circuits which covers each edge of G at least once (precisely k-times). It is obtained that every signed eulerian graph G has a circuit 6-cover, consisting of 4 circuit-covers of G, and as an immediate consequence, G has a circuit-cover with total number of edges at most . It is known that for every integer , there are infinitely many coverable signed graphs that have no circuit k-cover. Is it true that every coverable signed graph has a circuit 6-cover? This is still an open problem.


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