Topic
K-tree
About: K-tree is a research topic. Over the lifetime, 427 publications have been published within this topic receiving 12096 citations.
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TL;DR: In this article, the Hansen polytopes of split graphs were analyzed and shown to correspond to threshold graphs, and they were shown to have 3^d+16 nonempty faces.
Abstract: We analyze a remarkable class of centrally symmetric polytopes, the Hansen polytopes of split graphs. We confirm Kalai's 3^d-conjecture for such polytopes (they all have at least 3^d nonempty faces) and show that the Hanner polytopes among them (which have exactly 3^d nonempty faces) correspond to threshold graphs. Our study produces a new family of Hansen polytopes that have only 3^d+16 nonempty faces.
1 citations
Journal Article•
TL;DR: Based on network graph theory, using admittance product of k-tree branches in connected graph, the symbolic expression of network function and its sensitivity are presented and it is proved by the example that the method has validity and feasibility.
Abstract: The sensitivity analysis is important in electric network optimum design and tolerance analysis. The general method of sensitivity analysis is pure numerical calculation, their characteristics are completly numerical analysis one by one. Those methods inevitably exist computational complexity, such as redundant polynomials eliminating, needing more data memory capacity and calculation error. Based on network graph theory, using admittance product of k-tree branches in connected graph, the symbolic expression of network function and its sensitivity are presented. Comparing with incremental network method, the method is more fast and effective and is prone to program. It is proved by the example that the method has validity and feasibility.
1 citations
TL;DR: Graphs that have such 'chordal colorings' are weakly chordal graphs with simple forbidden subgraph characterizations, and such a chordal coloring of a graph G requires only @g(G) colors.
1 citations
TL;DR: In this paper, the possible densities of graphs in which each edge lies in at least two maximal cliques are found and the graphs of maximal densities are described, where each edge is associated with at least one maximal clique.
Abstract: Abstract The possible densities of graphs in which each edge lies in at least two maximal cliques are found and the graphs of maximal densities are described.
1 citations
TL;DR: The validity of the equality KG=K2G has been an open question and a graph in KG but not in K2G is exhibited here.
Abstract: Let G be the class of all graphs and K be the clique operator. The validity of the equality KG=K2G has been an open question for several years. A graph in KG but not in K2G is exhibited here.
1 citations