
Decomposing a graph into subgraphs with small components
The component size of a graph is the maximum number of edges in any conn...
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Dota Underlords game is NPcomplete
In this paper, we demonstrate how the problem of the optimal team choice...
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Generating subgraphs in chordal graphs
A graph G is wellcovered if all its maximal independent sets are of the...
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On the dichromatic number of surfaces
In this paper, we give bounds on the dichromatic number χ⃗(Σ) of a surfa...
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Tracking Paths in Planar Graphs
We consider the NPcomplete problem of tracking paths in a graph, first ...
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Efficiently Finding HigherOrder Mutants
Higherorder mutation has the potential for improving major drawbacks of...
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Discovering Domain Orders through Order Dependencies
Much realworld data come with explicitly defined domain orders; e.g., l...
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Computing Cliques and Cavities in Networks
Complex networks have complete subgraphs such as nodes, edges, triangles, etc., referred to as cliques of different orders. Notably, cavities consisting of higherorder cliques have been found playing an important role in brain functions. Since searching for the maximum clique in a large network is an NPcomplete problem, we propose using kcore decomposition to determine the computability of a given network subject to limited computing resources. For a computable network, we design a search algorithm for finding cliques of different orders, which also provides the Euler characteristic number. Then, we compute the Betti number by using the ranks of the boundary matrices of adjacent cliques. Furthermore, we design an optimized algorithm for finding cavities of different orders. Finally, we apply the algorithm to the neuronal network of C. elegans in one dataset, and find its all cliques and some cavities of different orders therein, providing a basis for further mathematical analysis and computation of the structure and function of the C. elegans neuronal network.
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