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David Wood, Tree densities of sparse graph classes

February 17 Wednesday @ 10:00 AM - 11:00 AM KST

Zoom ID: 934 3222 0374 (ibsdimag)

This talk considers the following question at the intersection of extremal and structural graph theory: What is the maximum number of copies of a fixed forest $T$ in an $n$-vertex graph in a graph class $\mathcal{G}$ as $n\to \infty$? I will answer this question for a variety of sparse graph classes $\mathcal{G}$. In particular, we show that the answer is $\Theta(n^{\alpha_d(T)})$ where $\alpha_d(T)$ is the size of the largest stable set in the subforest of $T$ induced by the vertices of degree at most $d$, for some integer $d$ that depends on $\mathcal{G}$. For example, when $\mathcal{G}$ is the class of $k$-degenerate graphs then $d=k$; when $\mathcal{G}$ is the class of graphs containing no $K_{s,t}$-minor ($t\geq s$) then $d=s-1$; and when $\mathcal{G}$ is the class of $k$-planar graphs then $d=2$. All these results are in fact consequences of a single lemma in terms of a finite set of excluded subgraphs. This is joint work with Tony Huynh (arXiv:2009.12989).

Details

Date:
February 17 Wednesday
Time:
10:00 AM - 11:00 AM KST
Event Category:
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Venue

Zoom ID: 934 3222 0374 (ibsdimag)

Organizer

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
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