Jinha Kim (김진하), On a conjecture by Kalai and Meshulam – the Betti number of the independence complex of ternary graphs

Room B232 IBS (기초과학연구원)

Given a graph G=(V,E), the independence complex of G is the abstract simplicial complex I(G) on V whose faces are the independent sets of G. A graph is ternary if it does not contain an induced cycle of length divisible by three. Kalai and Meshulam conjectured that if G is ternary then the sum of the Betti numbers

Jinha Kim (김진하), Independent domination of graphs with bounded maximum degree

Room B232 IBS (기초과학연구원)

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

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