演講公告

演講主題：Rainbow Spanning Trees in General Graphs
主講人：Paul Horn 教授 (Department of Mathematics at the University of Denver)
演講日期：2017年6月9日(星期五) 上午10:10 –11:00
演講地點：(光復校區) 科學一館213室
摘要內容：
Abstract. A beautiful conjecture of Brualdi and Hollingsworth states that if the even ordered complete graph K_2n is properly edge colored with 2n-1 colors, then the resulting graph can be decomposed into n edge disjoint rainbow spanning trees, that is spanning trees where each edge color appears exactly once in each tree. Recently, this conjecture has attracted a lot of attention; a result of the speaker states that one can find Omega(n) edge disjoint trees in this context with a very recent improvement on the implied constant by Pokrovskiy and Sudakov.
In general graphs, a proper edge coloring is not enough to imply the existence of even one such tree. But it is natural to ask what kinds of colorings and conditions on a graph imply the existence of many edge disjoint rainbow spanning trees. In this talk I’ll discuss a new result with my student Lauren Nelsen, in which we use a spectral condition to give a strong result in this direction. As part of a greater theme, I’ll give some examples of how spectral graph theory can play an important role in extremal graph theory in extending results valid for the complete graph into arbitrary host graphs.
相關檔案：Talk_20170609.pdf

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