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Journals and Conferences
A perfect matching in a 3-uniform hypergraph on n = 3k vertices is a subset of n3 disjoint edges. We prove that if H is a 3-uniform hypergraph on n = 3k vertices such that every vertex belongs to at least ( n−1 2 ) − ( 2n/3 2 ) + 1 edges then H contains a perfect matching. We give a construction to show that this result is best possible.
String kernel-based machine learning methods have yielded great success in practical tasks of structured/sequential data analysis. In this paper we propose a novel computational framework that uses general similarity metrics and distance-preserving embeddings with string kernels to improve sequence classification. An embedding step, a distance-preserving… (More)
A perfect matching in a 4-uniform hypergraph is a subset of b4 c disjoint edges. We prove that if H is a sufficiently large 4-uniform hypergraph on n = 4k vertices such that every vertex belongs to more than ( n−1 3 ) − ( 3n/4 3 ) edges then H contains a perfect matching. This bound is tight and settles a conjecture of Hán, Person and Schacht.
Evaluating an extremely useful graph property, the spectral radius (largest absolute eigenvalue of the graph adjacency matrix), for large graphs requires excessive computing resources. This problem becomes especially challenging, for instance with distributed or remote storage, when accessing the whole graph itself is expensive in terms of memory or… (More)
The problem of identifying important players in a given network is of pivotal importance for viral marketing, public health management, network security and various other fields of social network analysis. In this work we find the most important vertices in a graph G = (V,E) to immunize so as the chances of an epidemic outbreak is minimized. This problem is… (More)
Given a network of nodes, minimizing the spread of a contagion using a limited budget is a well-studied problem with applications in network security, viral marketing, social networks, and public health. In real graphs, virus may infect a node which in turn infects its neighbor nodes and this may trigger an epidemic in the whole graph. The goal thus is to… (More)
Recognition problems (Recog) are well studied in graph theory. For a fixed class C, Recog(C) asks whether a given graph belongs to C. For example, recognition of interval graphs (INT) can be done in a linear time. We introduce a new problem called partial representation extension (PRExt). For a given graph and a part of its representation fixed, it asks… (More)