K-tree

About: K-tree is a research topic. Over the lifetime, 427 publications have been published within this topic receiving 12096 citations.

The Diameter of Graphs of Convex Polytopes and f-Vector Theory.

Abstract: A train pulse generator has a memory for receiving and storing representations of numbers generated by the selective operation of a plurality of push button switches in accordance with selected numbers. Facilities, activated by the operation of any of the push button switches, operate the memory means to store the representations of the numbers in the memory. Other facilities sequentially apply representations of the stored representations to a register to activate a pulse generating oscillator which produces a train of pulses relating to a count of the register.

Efficient Enumeration of Maximal k-Plexes

Abstract: The problem of enumerating (i.e., generating) all maximal cliques in a graph has received extensive treatment, due to the plethora of applications in various areas such as data mining, bioinformatics, network analysis and community detection. However, requiring the enumerated subgraphs to be full cliques is too restrictive in common real-life scenarios where "almost cliques" are equally useful. Hence, the notion of a k-plex, a clique relaxation that allows every node to be "missing" k neighbors, has been introduced. But this seemingly minor relaxation casts existing algorithms for clique enumeration inapplicable, for inherent reasons. This paper presents the first provably efficient algorithms, both for enumerating the maximal k-plexes and for enumerating the maximal connected k-plexes. Our algorithms run in polynomial delay for a constant k and incremental FPT delay when k is a parameter. The importance of such algorithms is in the areas mentioned above, as well as in new applications. Extensive experimentation over both real and synthetic datasets shows the efficiency of our algorithms, and their scalability with respect to graph size, density and choice of k, as well as their clear superiority over the state-of-the-art.

On the tree representation of chordal graphs

Abstract: We introduce the notion of the boundary clique and the k-overlap clique graph and prove the following: Every incomplete chordal graph has two nonadjacent simplicial vertices lying in boundary cliques. An incomplete chordal graph G is k-connected if and only if the k-overlap clique graph gk(G) is connected. We give an algorithm to construct a clique tree of a connected chordal graph and characterize clique trees of connected chordal graphs using the algorithm.