### Paloma T. Lima, Graph Square Roots of Small Distance from Degree One Graphs

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Given a graph class $\mathcal{H}$, the task of the $\mathcal{H}$-Square Root problem is to decide whether an input graph G has a square root H that belongs to $\mathcal{H}$. We are interested in the parameterized complexity of the problem for classes $\mathcal{H}$ that are composed by the graphs at vertex deletion distance at most $k$

### Akanksha Agrawal, Polynomial Kernel for Interval Vertex Deletion

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Given a graph G and an integer k, the Interval Vertex Deletion (IVD) problem asks whether there exists a vertex subset S of size at most k, such that G-S is an interval graph. A polynomial kernel for a parameterized problem is a polynomial time preprocessing algorithm that outputs an equivalent instance of the problem whose size is bounded by

### Robert Ganian, Solving Integer Linear Programs by Exploiting Variable-Constraint Interactions

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Integer Linear Programming (ILP) is among the most successful and general paradigms for solving computationally intractable optimization problems in computer science. ILP is NP-complete, and until recently we have lacked a systematic study of the complexity of ILP through the lens of variable-constraint interactions. This changed drastically in recent years thanks to a series of results that together lay out a

### Gwenaël Joret, Packing and covering balls in graphs excluding a minor

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In 2007, Chepoi, Estellon, and Vaxès conjectured that there exists a universal constant $c>0$ such that the following holds for every positive integers $r$ and $k$, and every planar graph $G$: Either $G$ contains $k$ vertex-disjoint balls of radius $r$, or there is a subset of vertices of size at most $c k$ meeting all

### Nick Brettell, On the graph width parameter mim-width

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Maximum induced matching width, also known as mim-width, is a width parameter for graphs introduced by Vatshelle in 2012.  This parameter can be defined over branch decompositions of a graph G, where the width of a vertex partition (X,Y) in G is the size of a maximum induced matching in the bipartite graph induced by

### Sebastian Siebertz, Rank-width meets stability

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Forbidden graph characterizations provide a convenient way of specifying graph classes, which often exhibit a rich combinatorial and algorithmic theory. A prime example in graph theory are classes of bounded tree-width, which are characterized as those classes that exclude some planar graph as a minor. Similarly, in model theory, classes of structures are characterized by

### Luke Postle, Further progress towards Hadwiger’s conjecture

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In 1943, Hadwiger conjectured that every graph with no $K_t$ minor is $(t-1)$-colorable for every $t\ge 1$. In the 1980s, Kostochka and Thomason independently proved that every graph with no $K_t$ minor has average degree $O(t\sqrt{\log t})$ and hence is $O(t\sqrt{\log t})$-colorable.  Recently, Norin, Song and I showed that every graph with no $K_t$ minor is

### Zihan Tan, Towards Tight(er) Bounds for the Excluded Grid Theorem

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We study the Excluded Grid Theorem, a fundamental structural result in graph theory, that was proved by Robertson and Seymour in their seminal work on graph minors. The theorem states that there is a function $f$, such that for every integer $g > 0$, every graph of treewidth at least $f(g)$ contains the g×g-grid as a minor. For every

### Chun-Hung Liu (劉俊宏), Asymptotic dimension of minor-closed families and beyond

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The asymptotic dimension of metric spaces is an important notion in  geometric group theory. The metric spaces considered in this talk are  the ones whose underlying spaces are the vertex-sets of (edge-)weighted  graphs and whose metrics are the distance functions in weighted graphs.  A standard compactness argument shows that it suffices to consider the  asymptotic 기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209