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Da Qi Chen, Bipartite Saturation

Thursday, November 26, 2020 @ 10:00 AM - 11:00 AM KST

Zoom ID: 934 3222 0374 (ibsdimag)


Da Qi Chen
Carnegie Mellon University

In extremal graph theory, a graph G is H-saturated if G does not contain a copy of H but adding any missing edge to G creates a copy of H. The saturation number, sat(n, H), is the minimum number of edges in an n-vertex H-saturated graph. This class of problems was first studied by Zykov and Erdős, Hajnal, and Moon. They also determined the saturation number when H is a clique and classified the extremal structures.

In this talk, we will focus mainly on the bipartite saturation problem (which was also first introduced by Erdős, Hajnal, and Moon). Here, we always assume that both G and H are bipartite graphs. Then, G is H-saturated if G does not contain H but adding any missing edge across the bipartition creates a copy of H. We can then similarly define sat(n, H) as the minimum number of edges of an n-by-n bipartite graph that is also H-saturated. One of the most interesting and natural questions here is to determine the saturation number for the complete bipartite graph $K_{s, t}$. When s=t, the saturation number and its extremal structures were determined long ago but nothing else is known for the general case. Half a decade ago, Gan, Korandi, and Sudakov gave an asymptotically tight bound that was only off by an additive constant.  We will highlight the main ideas behind that proof and show, with some additional techniques, how the bound can be improved to achieve tightness for the case when s=t-1.

This talk is based on collaborative work with Debsoumya Chakraborti and Mihir Hasabnis. See arXiv: https://arxiv.org/abs/2009.07651 for the full paper.


Thursday, November 26, 2020
10:00 AM - 11:00 AM KST
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Zoom ID: 934 3222 0374 (ibsdimag)


O-joung Kwon (권오정)
IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209
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