10 events found.
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Jang Soo Kim (김장수), Longest elements in a semigroup of functions and Slater indices
Room B332 IBS (기초과학연구원)The group \( S_n \) of permutations on \(=\{1,2,\dots,n\} \) is generated by simple transpositions \( s_i = (i,i+1) \). The length \( \ell(\pi) \) of a permutation \( \pi \) is defined to be the minimum number of generators whose product is \( \pi \). It is well-known that the longest element in \( …
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IBS-DIMAG Winter School on Graph Minors, Week 2
Room B109 IBS (기초과학연구원) -
Jungho Ahn (안정호), A coarse Erdős-Pósa theorem for constrained cycles
Room B332 IBS (기초과학연구원)An induced packing of cycles in a graph is a set of vertex-disjoint cycles such that the graph has no edge between distinct cycles of the set. The classic Erdős-Pósa theorem shows that for every positive integer $k$, every graph contains $k$ vertex-disjoint cycles or a set of $O(k\log k)$ vertices which intersects every cycle of $G$. …
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IBS-DIMAG Winter School on Graph Minors, Week 3
Room B109 IBS (기초과학연구원) -
O-joung Kwon (권오정), Erdős-Pósa property of A-paths in unoriented group-labelled graphs
Room B332 IBS (기초과학연구원)A family $\mathcal{F}$ of graphs is said to satisfy the Erdős-Pósa property if there exists a function $f$ such that for every positive integer $k$, every graph $G$ contains either $k$ (vertex-)disjoint subgraphs in $\mathcal{F}$ or a set of at most $f(k)$ vertices intersecting every subgraph of $G$ in $\mathcal{F}$. We characterize the obstructions to …
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Sepehr Hajebi, The pathwidth theorem for induced subgraphs
Room B332 IBS (기초과학연구원)We present a full characterization of the unavoidable induced subgraphs of graphs with large pathwidth. This consists of two results. The first result says that for every forest H, every graph of sufficiently large pathwidth contains either a large complete subgraph, a large complete bipartite induced minor, or an induced minor isomorphic to H. The …
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Irene Muzi, An elementary bound for Younger’s conjecture
Room B332 IBS (기초과학연구원)In 1996, Reed, Robertson, Seymour and Thomas proved Younger's Conjecture, which states that for all directed graphs D, there exists a function f such that if D does not contain k disjoint cycles, D contains a feedback vertex set, i.e. a subset of vertices whose deletion renders the graph acyclic, of size bounded by f(k). …
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Johannes Carmesin, Open problems in graph theory
Room B332 IBS (기초과학연구원)Since the proof of the graph minor structure theorem by Robertson and Seymour in 2004, its underlying ideas have found applications in a much broader range of settings than their original context. They have driven profound progress in areas such as vertex minors, pivot minors, matroids, directed graphs, and 2-dimensional simplicial complexes. In this talk, …
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Michał Seweryn, Dimension and standard examples in planar posets
Room B332 IBS (기초과학연구원)The dimension of a poset is the least integer $d$ such that the poset is isomorphic to a subposet of the product of $d$ linear orders. In 1983, Kelly constructed planar posets of arbitrarily large dimension. Crucially, the posets in his construction involve large standard examples, the canonical structure preventing a poset from having small …