報 告 人：范更華 教授
報告題目：Circuit Covers in Signed Graphs
范更華，福州大學教授、博士生導師、曾任福州大學副校長以及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育部重點實驗室主任，1998年獲國家杰出青年科學基金，2003年獲教育部科技一等獎，2005年獲國家自然科學二等獎獲。主持多項國家自然科學基金重點項目與國家973計劃課題。主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、子圖覆蓋等方向的基礎理論研究。他的成果以“范定理”、“范條件”被國內外同行廣泛引用。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。
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.