Showing papers on "K-tree published in 1984"
TL;DR: These algorithms compare favorably with the fastest known algorithm for general graphs which has a worst-case running time of O(n ∗ e ∗ α) .
48 citations
TL;DR: This work presents linear time algorithms for computing the minimum number of complete subgraphs needed to cover or partition the edges of any simple graph G with maximal degree less than 5.
Abstract: We present linear time algorithms for computing the minimum number of complete subgraphs needed to cover or partition the edges of any simple graph G with maximal degree less than 5.
33 citations
TL;DR: In this paper, the authors build on results based on D.R. Fulkerson's anti-blocking polyhedral approach to perfect graphs to obtain information about critical perfect graphs and related clique-generated graphs.
Abstract: Publisher Summary This chapter builds on results based on D.R. Fulkerson's anti-blocking polyhedral approach to perfect graphs to obtain information about critical perfect graphs and related clique-generated graphs. Fulkerson felt that a proof of the perfect graph theorem would involve exactly the kind of duality that existed in his theory of blocking and anti-blocking polyhedral. A critical perfect graph—p-critical for short—is an imperfect graph all of whose proper induced subgraphs are perfect. A p-critical graph with n vertices has exactly n cliques of size ω (G) with each vertex in ω (G) maximal cliques and has exactly n stable sets of size α (G) with each vertex in α (G) maximal stable sets. Each maximal clique intersects all but one maximal stable sets, and vice versa. If G is a pseudo-p-critical graph, each maximal clique in M (G) corresponds to a vertex of G.
22 citations
TL;DR: It is shown that a certain class of (0–1) polyhedra, which includes the matroid basis poly topes and the perfect matching polytopes, have graphs with the property that the edges, under a certain condition, belong to cycles of every length l ≥ 3, and the others tocycles of everylength l ≥ 4.
10 citations