Mathematical Sciences: Circuit Covers and Integer Flows - Research in Graph Theory

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This award supports the research of Professor Zhang to work in combinatorics. The investigator will continue his investigations in the topics of circuit covers, circuit decompositions, integer flows, and edge-colorings of graphs. The major targets in this project will be the circuit double cover conjecture and integer flow problems together with some related problems, including the question of 3-edge-coloring for some families of graphs. The research is in the general area of combinatorics.Combinatorics attempts to find efficient methods to study how discrete collections can be organized. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, as in telephone systems, and the design of algorithms in computer science all deal with discrete objects, and this makes use of combinatorial research.