Topic
K-tree
About: K-tree is a research topic. Over the lifetime, 427 publications have been published within this topic receiving 12096 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: The problem of determining whether a graph has a K i -cover ( i ⩾ 2) of cardinality ⩽ k is shown to be NP-complete for graphs in general and polynomial algorithms for solving the separation problem for some classes of facets of the Ki -cover polytope are described.
27 citations
TL;DR: A simple unified algorithmic process which uses either LexBFS or MCS on a chordal graph to generate the minimal separators and the maximal cliques in linear time in a single pass is presented.
27 citations
TL;DR: An important family of graphs is introduced which is closed under the clique operator and contains clique divergent graphs with strictly linear growth, i.e., o(knG) = o(G) + rn, where r is any fixed positive integer.
27 citations
TL;DR: A conjecture about 4-connected maximal planar graphs that implies the original conjecture and a weaker form of the conjecture in which outerplanar sub graphs are replaced by subgraphs with no homeomorphs ofK4 is verified.
27 citations
TL;DR: In this paper, it was shown that the Alexander dual of the clique complex of any chordal graph is vertex decomposable and that all powers of the vertex cover ideal of such graphs have linear quotients.
Abstract: In this article, Cohen–Macaulay chordal graphs and generalized star graphs are studied to show that all powers of the vertex cover ideal of such graphs have linear quotients. Moreover, it is shown that the Alexander dual of the clique complex of any chordal graph is vertex decomposable.
26 citations