Decomposition of Complete Graphs into Paths and Stars with Different Number of Edgesdoi:10.61091/jcmcc122-25Graph decompositionPathsStarsComplete graphLet \\(P_n\\) and \\(K_n\\) respectively denote a path and complete graph on \\(n\\) vertices. By a \\(\\{pH_{1}, qH_{2}\\}\\...
We study the complete graph equipped with a topology induced by independent and identically distributed edge weights. The focus of our analysis is on the weight W n and the number of edges H n of the minimal weight path between two distinct vertices in the weak disorder regime. We establish...
GraphTheory CompleteGraph construct complete graph Calling Sequence Parameters Options Description Examples Compatibility Calling Sequence CompleteGraph( n , opts ) CompleteGraph( V , opts ) CompleteGraph( n , m , opts ) CompleteGraph( n1 , n2 ,...,...
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $f$ be a 0-1 labeling of $E(G)$ so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling $f$ \\emph{edge-friendly}. The \\emph{edge-...
Here ex(n,F) is the Turán number of F, which is the maximum number of edges of a simple graph of order n having no member of F as a subgraph. This determined ar(Kn,G) asymptotically when χ(H)≥3 for any H∈G. The remaining case is more complex. For paths, Simonovits and ...
In an edge-colored graph G, let dmon(v) denote the maximum number of edges with the same color incident with a vertex v in G, called the monochromatic-degree of v. The maximum value of dmon(v) over all vertices v∈V(G) is called the maximum monochromatic-degree of G, denoted by...
be an edge-coloured complete graph on n vertices. Let ∆ mon (K c n ) denote the maximum number of edges of the same colour incident with a vertex of K c n . Equivalently, ∆ mon (K c n ) = max ∆(H) over all monochromatic subgraphs H in K c n . Daykin [8] asked ...
A c-monotone drawing is generalized twisted if there is a ray emanating from O that crosses all the edges of the drawing. Via this class of drawings, we show that every simple drawing of the complete graph with n vertices contains (n 1 2 ) pairwise disjoint edges and a plane cycle (...
Suppose that in a complete graph on N points, each edge is given arbitrarily either the color red or the color blue, but the total number of blue edges is ... AW Goodman - 《Journal of the Australian Mathematical Society》 被引量: 45发表: 1985年 On small graphs with forced monochromatic...
edges[i].length == 2 0 <= ai, bi<= n - 1 ai!= bi There are no repeated edges. Accepted 136.8K Find the connected components of an undirected graph using depth-first search (DFS) or breadth-first search (BFS). Hint 2 For each connected component, count the number of nodes and ...