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DTSTART:20210101T000000
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DTSTART;TZID=Asia/Seoul:20220215T163000
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SUMMARY:Jinha Kim (김진하)\, Independent domination of graphs with bounded maximum degree
DESCRIPTION:An independent dominating set of a graph\, also known as a maximal independent set\, is a set $S$ of pairwise non-adjacent vertices such that every vertex not in $S$ is adjacent to some vertex in $S$. We prove that for $\Delta=4$ or $\Delta\ge 6$\, every connected $n$-vertex graph of maximum degree at most $\Delta$ has an independent dominating set of size at most $(1-\frac{\Delta}{ \lfloor\Delta^2/4\rfloor+\Delta })(n-1)+1$. In addition\, we characterize all connected graphs having the equality and we show that other connected graphs have an independent dominating set of size at most $(1-\frac{\Delta}{ \lfloor\Delta^2/4\rfloor+\Delta })n$.\nThis is joint work with Eun-Kyung Cho\, Minki Kim\, and Sang-il Oum.
URL:https://dimag.ibs.re.kr/event/2022-02-15/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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