报 告 人：范更华 教授
报告题目：Circuit Covers in Signed Graphs
范更华，福州大学教授、博士生导师、曾任福州大学副校长以及全国组合数学与图论学会理事长，现任离散数学及其应用教育部重点实验室主任，1998年获国家杰出青年科学基金，2003年获教育部科技一等奖，2005年获国家自然科学二等奖获。主持多项国家自然科学基金重点项目与国家973计划课题。主要从事图论领域中的结构图论、极图理论、带权图、欧拉图、整数流理论、子图覆盖等方向的基础理论研究。他的成果以“范定理”、“范条件”被国内外同行广泛引用。一些成果还作为定理出现在国外出版的教科书中。担任国际图论界权威刊物《Journal of Graph Theory》执行编委。
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.