Leírás
The program.
2pm: Wei-Tian Li (Taiwan), Ramsey-Type of Problems on Posets in the Boolean Lattices
2:30: Zhiyu Wang (Columbia, SC, USA)
3:00-3:15 break
3:15: Sean English (Western Michigan U., Kalamazoo, USA), Randomly Playing Plates and Olives
3:45: Attila Dankovics (London)
See the abstracts below or in the attachment.
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Wei-Tian Li
Ramsey-Type of Problems on Posets in the Boolean Lattices
Abstract. A family F of subsets of [n]:={1,…,n}is said to be a copy of a poset P, if there
is a bijection ffrom Pto Fsuch that x≤Py if and only if f(x)⊆f(y). k-coloring on the Boolean
lattice Bnis a function c from Bn to [k]. In this talk, we study the colorings on the Boolean lattices,
and present some results on the existence a monochromatic copy of the given posets, or a rainbow
copy of them.
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Zhiyu Wang
Title: Color-disjoint rainbow spanning trees of edge-colored graphs Abstract: For any $t\geq 1$ and an edge-colored multigraph $G$, we show that $G$ has $t$ color-disjoint rainbow spanning trees if and only if for any partition $P$ of $V(G)$, there are at least $t(|P|-1)$ distinct colors occurring in the crossing edges of $P$. Our theorem generalizes two previous results: Nash-Williams-Tutte theorem and Schrijver's theorem. As an application, we resolve a conjecture of Jahanbekam and West: $r(n,t)={n-2 \choose 2}+t$ whenever $n\geq 2t+2 \geq 6$. Here $r(n,t)$ is the maximum number of colors in an edge-coloring of $K_n$ not having $t$ edge-disjoint rainbow spanning trees. ********************************************* Attila Dankovics
title: Low independence number and Hamiltonicity implies pancyclicity
abstract: Given a Hamiltonian graph $G$ with independence number at most $k$ we are looking for the minimum number of vertices $f(k)$ that guarantees that $G$ is pancyclic. The problem of finding $f(k)$ was raised by Erdős who showed that $f(k)\le 4k^4$, and conjectured that $f(k)=\Theta(k^2)$. Formerly the best known upper bound was $f(k)=O(k^{7/3})$ by Lee and Sudakov. We improve this bound and show that $f(k)=O(k^{11/5})$.