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Hitting minors on bounded treewidth graphs. III. Lower bounds
In particular, we prove that when ${\cal F}$ contains a single connected graph $H$ that is either $P_5$ or is not a minor of the banner (that is, the graph consisting of a $C_4$ plus a pendent edge), then $f_{{\cal F}}(tw)= 2^{\Omega(tw \cdot \log tw)}$.
Data Structures and Algorithms Computational Geometry Discrete Mathematics Combinatorics 05C85, 68R10, 05C75, 05C83, 05C75, 05C69 G.2.2; F.2.2
Hitting minors on bounded treewidth graphs. II. Single-exponential algorithms
${\cal F}$-TM-DELETION) problem consists in, given a graph $G$ and an integer $k$, decide whether there exists $S \subseteq V(G)$ with $|S| \leq k$ such that $G \setminus S$ does not contain any of the graphs in ${\cal F}$ as a minor (resp.
Data Structures and Algorithms Computational Complexity Discrete Mathematics Combinatorics 05C85, 68R10, 05C75, 05C83, 05C75, 05C69 G.2.2; F.2.2
A Neighborhood-preserving Graph Summarization
Since many graph algorithms are based on the neighborhood information available for each node, the idea is to produce a smaller graph which can be used to allow these algorithms to handle large graphs and run faster while providing good approximations.
Graph Classification
Data Structures and Algorithms
Discrete Mathematics
Social and Information Networks
Hitting minors on bounded treewidth graphs. IV. An optimal algorithm
For a fixed finite collection of graphs ${\cal F}$, the ${\cal F}$-M-DELETION problem asks, given an $n$-vertex input graph $G,$ for the minimum number of vertices that intersect all minor models in $G$ of the graphs in ${\cal F}$.
Data Structures and Algorithms Computational Complexity Combinatorics 05C85, 68R10, 05C75, 05C83, 05C75, 05C69 G.2.2; F.2.2
