On the generation of the chordless four-cycle
نویسنده
چکیده
So-called full line concentration graphs represent a set of random variables by the vertices of an undirected graph. That is, some, but in general not all, pairs of vertices are joined by edges and a missing edge between, say, vertices i and j implies that the corresponding random variables are conditionally independent given all remaining variables. If the joint distribution is multivariate Gaussian a missing edge corresponds to a zero in the concentration matrix, i.e. in the inverse covariance matrix, ∗Version submitted to Biometrika
منابع مشابه
Erd\H{o}s-P\'osa property of chordless cycles and its applications
A chordless cycle in a graph G is an induced subgraph of G which is a cycle of length at least four. We prove that the Erdős-Pósa property holds for chordless cycles, which resolves the major open question concerning the Erdős-Pósa property. Our proof for chordless cycles is constructive: in polynomial time, one can find either k + 1 vertex-disjoint chordless cycles, or ck 2 log k vertices hitt...
متن کاملPolynomial enumeration of chordless cycles on cyclically orientable graphs
In a finite undirected simple graph, a chordless cycle is an induced subgraph which is a cycle. A graph is called cyclically orientable if it admits an orientation in which every chordless cycle is cyclically oriented. We propose an algorithm to enumerate all chordless cycles of such a graph. Compared to other similar algorithms, the proposed algorithm have the advantage of finding each chordle...
متن کاملSlightly triangulated graphs are perfect
A graph is triangulated if it has no chordless cycle with at least four vertices (8k 4; C k 6 6 G). These graphs have been generalized by R. Hayward with the weakly triangulated graphs (8k 5; C k ; C k 6 6 G). In this note we propose a new generalization of triangulated graphs. A graph G is slightly triangulated if it satisses the two following conditions : 1. G contains no chordless cycle with...
متن کاملAn Efficient Algorithm for Enumerating Chordless Cycles and Chordless Paths
A chordless cycle (induced cycle) C of a graph is a cycle without any chord, meaning that there is no edge outside the cycle connecting two vertices of the cycle. A chordless path is defined similarly. In this paper, we consider the problems of enumerating chordless cycles/paths of a given graph G = (V,E), and propose algorithms taking O(|E|) time for each chordless cycle/path. In the existing ...
متن کاملشبیهسازی و بهینهسازی اگزرژی- اقتصادی یک سیستم تولید سهگانه
In this study, a combination of micro gas turbine, absorption cooling, and organic rankine cycle is selected. The system is modeled applying the laws of thermodynamic, and based on this model, exergy and economic analyses are performed for each component of the system. Four design variables, namely compressor pressure ratio, turbine inlet temperature, turbine efficiency, and compressor efficien...
متن کامل