[2017 Discrete Math 세미나]

** Date: ** 2017-12-28

**Speaker :** Jaehoon Kim (Birmingham University, UK)

**Abstract : **A classical result of Komlós, Sárközy and Szemerédi states that every n-vertex graph with minimum degree at least (1/2 +o(1))n contains every n-vertex tree with maximum degree at most O(n/log n) as a subgraph, and the bounds on the degree conditions are sharp.
On the other hand, Krivelevich, Kwan and Sudakov recently proved that for every n-vertex graph G with minimum degree at least αn for any fixed α>0 and every n-vertex tree T with bounded maximum degree, one can still find a copy of T in G with high probability after adding O(n) randomly-chosen edges to G.
We extend this result to trees with unbounded maximum degree. More precisely, for a given nε ≤ Δ≤ cn/log n and α>0, we determined the precise number (up to a constant factor) of random edges that we need to add to an arbitrary n-vertex graph G with minimum degree αn in order to guarantee with high probability a copy of any fixed T with maximum degree at most Δ. This is joint work with Felix Joos.

**VOD : **[VIDEO] [YOUTUBE]

Information Center for Mathematical Sciences KAIST

34141 대전광역시 유성구 대학로 291 (구성동373-1)

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전화 042-350-8196

e-mail : mathnet@mathnet.or.kr

Copyright (C) 2018. ICMS All Rights Reserved.

34141 대전광역시 유성구 대학로 291 (구성동373-1)

한국과학기술원(KAIST) 수리과학정보센터

전화 042-350-8196

e-mail : mathnet@mathnet.or.kr

Copyright (C) 2018. ICMS All Rights Reserved.