Multipartite graph - Wikipedia
In graph theory, a part of mathematics, a k-partite graph is a graph whose vertices are (or can be) partitioned into k different independent sets. Equivalently, it is a graph that can be colored with k colors, so that no two endpoints of an edge have the same color. When k = 2 these are the bipartite graphs, and when k = 3 they are called the ...
Complete k-Partite Graph -- from Wolfram MathWorld
4 天之前 · A complete -partite graph is a k-partite graph (i.e., a set of graph vertices decomposed into disjoint sets such that no two graph vertices within the same set are adjacent) such that every pair of graph vertices in the sets are adjacent.
Multipartite graphs which are not planar - Mathematics Stack Exchange
A multipartite graph is a graph of the form $K_{r_1,\ldots, r_n}$ where $n > 1$, $r_1, \ldots, r_n\ge 1$, such that The set of nodes of the graph is the disjoint union of n sets: $V = V_1 \cup\cdots\cup V_n$, and $|V_i|=r_i$ for all $1\le i\le n$.
Unsupervised Keyphrase Extraction with Multipartite Graphs
2018年3月23日 · We propose an unsupervised keyphrase extraction model that encodes topical information within a multipartite graph structure. Our model represents keyphrase candidates and topics in a single graph and exploits their mutually reinforcing relationship to …
Proving complete multipartite graph - Mathematics Stack Exchange
2021年9月13日 · Suppose a graph $G=(V,E)$ has the property that if $uv \notin E, vw\notin E\implies uw\notin E$. If this property holds then prove that it is a complete multipartite graph. Now I am thinking to take the complement of a complete multipartite graph, which is a couple of complete isolated graphs. So, will the property also hold when I take the ...
Eigenvalues of complete multipartite graphs - ScienceDirect
2012年9月6日 · The complete multipartite graph K p 1, p 2, …, p k is a graph on n = ∑ i = 1 k p i vertices. The set of vertices is partitioned into parts of cardinalities p 1, p 2, …, p k; an edge joins two vertices if and only if they belong to different parts.
Complete subgraphs in a multipartite graph | Combinatorics, …
In this article, we investigate the r> t + 1 case of the problem, which has remained dormant for over 40 years. We resolve the problem exactly in the case when r ≡ − 1 (mod t) , and up to an additive constant for many other cases, including when r ≥ (3t − 1)(t − 1) .
Problem : Determine the exact threshold numbers of the complete multipartite graphs. Conjecture : orF all even n≥2, there is a graph Gwith Θ(G) = nand Θ(Gc) = n+1. This is equialenvt to that for all odd n≥3, there is a graph Gwith Θ(G) = nand Θ(Gc) = n−1, where Gc is the complement of G.
The genus of the complete multipartite graph and the complete …
These two kinds of graphs have recursive structure and offer a very flexible choice of network size with respect to a fixed network order. This paper addresses the genus of the complete multipartite graph and the complete multi-layered graph which measures how efficiently we can set up a computer network using these graph layouts.
MAXIMUM MATCHINGS IN COMPLETE MULTIPARTITE GRAPHS DAVID SITTON Abstract. How many edges can there be in a maximum matching in a com-plete multipartite graph? Several cases where the answer is known are dis-cussed, and then a new formula is given which answers this question. 1. Introduction Supposewehaveacompanythathasseveraldepartments ...
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