CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Yuqing Lin, School of Electrical Engineering and Computer Science, The University of Newcastle Title: Edge disjoint perfect matchings in regular graph Location: Room V31, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 13th Aug 2015 Abstract: Existing of perfect matchings in regular graph is a fundamental problem in graph theory, and it closely model many real world problems such as broadcasting and network management. Recently, we have studied the number of edge disjoint perfect matching in regular graph, and using some well-known results on the existence of perfect matching and operations forcing unique perfect matchings in regular graph, we are able to make some pleasant progress. In this talk, we will present the new results and briefly discuss the proof. [Permanent link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Yuqing Lin, School of Electrical Engineering and Computer Science, The University of Newcastle Title: The number of maximal state circles of plane graphs Location: Room V106, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 2:00 pm, Thu, 5th Mar 2015 Abstract: It is well known that there is a one-to-one correspondence between signed plane graphs and link diagrams via the medial construction. The relationship was once used in knot tabulations in the early time of study in knot theory. Indeed, it provides a method of studying links using graphs. Let $G$ be a plane graph. Let $D(G)$ be the alternating link diagram corresponding to the (positive) $G$ obtained from the medial construction. A state $S$ of $D$ is a labeling each crossing of $D$ by either $A$ or $B$. Making the corresponding split for each crossing gives a number of disjoint embedded closed circles, called state circles. We call a state which possesses maximum number of state circles a maximum state. The maximum state is closely related to the genus of the corresponding link, thus has been studied. In this talk, we will discuss some of the recent progress we have made on this topic. [Permanent link]