Da Qi Chen

Da Qi Chen
Carnegie Mellon University | CMU · Department of Mathematical Sciences

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8
Publications
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Publications

Publications (8)
Article
We consider the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We introduce and study a general downgrading variant of the interdiction problem where the capacity of an arc is a function of the subset of its endpoints that are d...
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The minimum spanning tree of a graph is a well-studied structure that is the basis of countless graph theoretic and optimization problem. We study the minimum spanning tree (MST) perturbation problem where the goal is to spend a fixed budget to increase the weight of edges in order to increase the weight of the MST as much as possible. Two popular...
Article
Generalized Turán problems have been a central topic of study in extremal combinatorics throughout the last few decades. One such problem, maximizing the number of cliques of a fixed order in a graph with fixed number of vertices and bounded maximum degree, was recently completely resolved by Chase. Kirsch and Radcliffe raised a natural variant of...
Article
This paper considers an edge minimization problem in saturated bipartite graphs. An n by n bipartite graph G is H-saturated if G does not contain a subgraph isomorphic to H but adding any missing edge to G creates a copy of H. More than half a century ago, Wessel and Bollobas independently solved the problem of minimizing the number of edges in K(s...
Preprint
Full-text available
This paper considers an edge minimization problem in saturated bipartite graphs. An $n$ by $n$ bipartite graph $G$ is $H$-saturated if $G$ does not contain a subgraph isomorphic to $H$ but adding any missing edge to $G$ creates a copy of $H$. More than half a century ago, Wessel and Bollob\'as independently solved the problem of minimizing the numb...
Preprint
Full-text available
Generalized Tur\'an problems have been a central topic of study in extremal combinatorics throughout the last few decades. One such problem, maximizing the number of cliques of size $t$ in a graph of a fixed order that does not contain any path of a given length, was recently considered and asymptotically solved by Luo. We fully resolve this proble...
Preprint
Full-text available
Generalized Tur\'an problems have been a central topic of study in extremal combinatorics throughout the last few decades. One such problem, maximizing the number of cliques of a fixed order in a graph with fixed number of vertices and bounded maximum degree, was recently completely resolved by Chase. Kirsch and Radcliffe raised a natural variant o...
Preprint
We study the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We show hardness of obtaining strictly unicriterion approximations for this basic vertex interdiction problem. We also introduce and study a general downgrading variant...

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