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DTSTART:20190101T000000
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DTSTART;TZID=Asia/Seoul:20200602T163000
DTEND;TZID=Asia/Seoul:20200602T173000
DTSTAMP:20260420T045403
CREATED:20200528T061536Z
LAST-MODIFIED:20240705T200043Z
UID:2491-1591115400-1591119000@dimag.ibs.re.kr
SUMMARY:Huy-Tung Nguyen\, The average cut-rank of graphs
DESCRIPTION:The cut-rank of a set X of vertices in a graph G is defined as the rank of the X×(V(G)∖X) matrix over the binary field whose (i\,j)-entry is 1 if the vertex i in X is adjacent to the vertex j in V(G)∖X and 0 otherwise. We introduce the graph parameter called the average cut-rank of a graph\, defined as the expected value of the cut-rank of a random set of vertices. We show that this parameter does not increase when taking vertex-minors of graphs and a class of graphs has bounded average cut-rank if and only if it has bounded neighborhood diversity. This allows us to deduce that for each real α\, the list of induced-subgraph-minimal graphs having average cut-rank larger than (or at least) α is finite. We further refine this by providing an upper bound on the size of obstruction and a lower bound on the number of obstructions for average cut-rank at most (or smaller than) α for each real α≥0. Finally\, we describe explicitly all graphs of average cut-rank at most 3/2 and determine up to 3/2 all possible values that can be realized as the average cut-rank of some graph. This is joint work with Sang-il Oum.
URL:https://dimag.ibs.re.kr/event/2020-06-02/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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