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Minho Cho (조민호), Strong Erdős-Hajnal property on chordal graphs and its variants

June 13 Tuesday @ 4:30 PM - 5:30 PM KST

Room B332, IBS (기초과학연구원)

Speaker

Minho Cho (조민호)
IBS Extremal Combinatorics and Probability Group

A graph class $\mathcal{G}$ has the strong Erdős-Hajnal property (SEH-property) if there is a constant $c=c(\mathcal{G}) > 0$ such that for every member $G$ of $\mathcal{G}$, either $G$ or its complement has $K_{m, m}$ as a subgraph where $m \geq \left\lfloor c|V(G)| \right\rfloor$. We prove that the class of chordal graphs satisfies SEH-property with constant $c = 2/9$.

On the other hand, a strengthening of SEH-property which we call the colorful Erdős-Hajnal property was discussed in geometric settings by Alon et al.(2005) and by Fox et al.(2012). Inspired by their results, we show that for every pair $F_1, F_2$ of subtree families of the same size in a tree $T$ with $k$ leaves, there exist subfamilies $F’_1 \subseteq F_1$ and $F’_2 \subseteq F_2$ of size $\theta \left( \frac{\ln k}{k} \left| F_1 \right|\right)$ such that either every pair of representatives from distinct subfamilies intersect or every such pair do not intersect. Our results are asymptotically optimal.

Joint work with Andreas Holmsen, Jinha Kim and Minki Kim.

Details

Date:
June 13 Tuesday
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:
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Venue

Room B332
IBS (기초과학연구원) + Google Map

Organizer

Sang-il Oum (엄상일)
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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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