trees (mathematics)/ tree decompositiongraphstreesedgesdecomposition/ B0250 Combinatorial mathematics C1160 Combinatorial mathematicsLet H be a tree on hges2 vertices. It is shown that if G=(V, E) is a graph wit
A tree decomposition of graphG = (V, E) is referred to as a partition of edge setE into edge-disjoint trees. Given (not necessarily distinct) vertices u1, u2 ⋯ uk∈V with k⩾2, a sufficient and necessary condition is given for a connected graphG = (V, E) to have a tree dec...
The length of a tree-decomposition of a graph is the maximum distance (in the graph) between two vertices of a same bag of the decomposition. The treelength of a graph is the minimum length among its tree-decompositions. Treelength of graphs has been studied for its algorithmic applications...
We study in this paper the problem of computing a tree-decomposition of a graph with width at most k and minimum number of bags. More precisely, we focus on the following problem: given a fixed k≥1, what is the complexity of computing a tree-decomposition of width at most k with mini...
decomposition of adhesion less than k of G in which this k-block appears as a part.Carmesin et al. proved that every fi nite graph has a canonical tree-decomposition of adhesion less than k that distinguishes all its k-blocks and tangles of order k. We construct such tree-decompositions ...
A tree decomposition of a graph G is a pair (X , T ), where T is a tree and X = {Xi | i ∈ V (T )} is a collection of subsets of V (G) such that • i∈V (T ) Xi = V (G), • for each edge {u, v} ∈ E(G), there is a node i ∈ V (T ) such ...
A tree decomposition of a graph satisfies the following −Each node of the graph must be part of at least one "bag" in the tree decomposition. If two nodes are connected by an edge, there must be at least one "bag" containing both nodes. The nodes present in a bag must form a ...
A directed graph is indecomposable if all its intervals are trivial. Given an integer k > 0, a directed graph G = (V,A) is called an indecomposable k-covering provided that for every subset X of V with |X| ≤ k, there exists a subset Y of V such that X ⊆ Y, G[Y] is ...
Decision trees, Decision matrix, T Chart, Influence diagrams, which are powerful in questions of decision making, holding decision tree analysis and Analytic Hierarchy Process (AHP), visual decomposition the decision problem into hierarchy of easily comprehensible sub-problems and solving them without an...
A tree decomposition of a graph G=(V,E) is a pair 〈{Xi∣i∈I},T〉, where each Xi is a subset of V, called a bag, and T=(I,F) is a tree with node set I and edge set F. The following must hold: The width of 〈{Xi∣i∈I},T〉 is max{|Xi|∣i∈I}−1. The ...