기초과학연구원 이산수학그룹
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A celebrated result of Bayer and Stillman from 1987 states that for a homogeneous ideal $I$ of a polynomial ring $S$, the regularities of $S/I$ and $S/\textrm{GIN}(I)$ are the same under the reverse lexicographic monomial ordering, where $\textrm{GIN}(I)$ is the generic initial ideal. If $R$ is a polynomial ring whose variables are subdivided into disjoint … |
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Treewidth is a graph parameter commonly used to quantify how "close" a graph is to a tree. Although it is a cornerstone of structural graph theory and algorithm design, it is nearly useless for algorithmic purposes in many dense graph classes. In this talk, we discuss the tree-independence number, a more versatile graph parameter that … |
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We say a graph $G$ is $(2,m)$-linked if, for every choice of $m+2$ distinct vertices $a_1,\ldots,a_m,b_1,b_2$ in $G$, there exist two vertex-disjoint connected subgraphs $A$ and $B$ of $G$ such that $\{a_1,\ldots,a_m\}\subseteq V(A)$ and $\{b_1,b_2\}\subseteq V(B)$. A related notion is $k$-linkedness: a graph is $k$-linked if, for any distinct vertices $s_1,\ldots,s_k,t_1,\ldots,t_k$, it contains $k$ pairwise … |
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