Dong Yeap Kang (강동엽), A proof of the Erdős-Faber-Lovász conjecture

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A hypergraph is linear if every pair of two distinct edges shares at most one vertex. A longstanding conjecture by Erdős, Faber, and Lovász in 1972, states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. In this talk, I will present the ideas to prove the conjecture for

Ron Aharoni, Colorful KKM and multiple cakes division

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In the "cake partition" problem n players have each a list of preferred parts for any partition of the interval ("cake") into n sub-intervals. Woodall, Stromquist and Gale proved independently that under mild conditions on the list of preferences (like continuity) there is always a partition and assignment of parts to the players, in which every player gets

Jie Ma (马杰), Non-repeated cycle lengths and Sidon sequences

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We prove a conjecture of Boros, Caro, Furedi and Yuster on the maximum number of edges in a 2-connected graph without repeated cycle lengths, which is a restricted version of a longstanding problem of Erdos. Our proof together with the matched lower bound construction of Boros, Caro, Furedi and Yuster show that this problem can

David Wood, Tree densities of sparse graph classes

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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

Yixin Cao (操宜新), Recognizing (unit) interval graphs by zigzag graph searches

Room B232 IBS (기초과학연구원)

Corneil, Olariu, and Stewart presented a recognition algorithm for interval graphs by six graph searches. Li and Wu simplified it to only four. The great simplicity of the latter algorithm is however eclipsed by the complicated and long proofs. The main purpose of this paper is to present a new and significantly shorter proof for

Édouard Bonnet, Twin-width and ordered binary structures

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The twin-width of a graph G can be defined as the least integer d such that there is a sequence of length |V(G)| of (strictly) coarser and coarser partitions of its vertex set V(G), and every part X of every partition P of the sequence has at most d other parts Y of P with

Sophie Spirkl, Pure pairs in ordered graphs

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A pure pair in a graph G is a pair of subsets A, B of the vertex set of G such that in G, either all of the edges or none of the edges between A and B are present. Pure pairs have been studied recently motivated by their connections to the Erdos-Hajnal conjecture. In

István Tomon, Ramsey properties of semilinear graphs

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A graph $G$ is semilinear of bounded complexity if the vertices of $G$ are elements of $\mathbb{R}^{d}$, and the edges of $G$ are defined by the sign patterns of $t$ linear functions, where $d$ and $t$ are constants. In this talk, I will present several results about the symmetric and asymmetric Ramsey properties of semilinear

IBS 이산수학그룹 Discrete Mathematics Group
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