So, with all these definitions, what is a complete graph? A complete graph is a graph in which each vertex is connected to every other vertex. That is, a complete graph is an undirected graph where every pair of distinct vertices is connected by a unique edge. This is the complete graph...
We prove that ω 2(G n ) = 0 for any spatial complete graph G n with n ≥ 7 vertices, where ω 2 is the function introduced by J.Y. Conway and C. McA. Gordon in 1983. Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 13...
给定一个n个顶点的无向完全图。...对于每一组顶点S,满足|S|≥2,S要么是红色连通的,要么是蓝色连通的,但不能既是红色连通又是蓝色连通。请计算出涂色的方案数,并将其对 998244353 取模后输出。
cyclesIn this paper we find the maximum number of pairwise edge-disjoint m-cycles which exist in a complete graph with n vertices, for all values of n and m with 3≤m≤n. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:1-7, 2011Daniel...
A connected graph is a graph where a path of distinct edges exists for each pair of vertices that connects them. There is no vertex, edge, or collection of vertices and edges that are not connected to the rest of the graph. What is the difference between a connected and a complete graph...
Clearly, a Λ2∗-graph is a Λ2-graph. We prove the converse by contradiction. Let G=(V,E) be a Λ2-graph and assume that G is not a Λ2∗-graph. Then, there are nonadjacent vertices x and y in G with κ˜∗(x,y)≥3. Let S be a minimal x,y-cut with at least...
be the complete graph, with vertices \(v_n=\{1,\dotsc ,n\}\) and edges \(e_n=\big \{\{i,j\}:1\le i<j\le n\big \}\) . with each edge we associate an independent poisson point process on the time interval \([0,\beta /n]\) with two kinds of outcomes: ‘crosses’ ...
Intrinsically knotted graphs In 1983, Conway and Gordon [J Graph Theory 7 (1983), 445–453] showed that every (tame) spatial embedding of K7, the complete graph on 7 vertices, contains... J Foisy - 《Journal of Graph Theory》 被引量: 102发表: 2002年 ...
In Sim, two players compete on a complete graph of six vertices (K 6). The players alternate in coloring one as yet uncolored edge using their color. The player who first completes a monochromatic triangle (K 3) loses. Replacing K 6 and K 3 by arbitrary graphs generalizes Sim to graph...
1b. According to [2], this scheme yields an embedding for the complete graph with the largest possible number of vertices. Unfortunately, due to broken physical vertices the shown templates are not applicable in real hardware. Thus, in [13] an algorithm was proposed trying to extract a ...