graph-decompositionsLet Cand Sdenote a cycle and a star on m edges, respectively. We investigate the decomposition of the complete graphs, K, into cycles and stars on the same number of edges. We give an algorithm that determines values of n, for a given value of m, where Kis {C, S...
The line segments between points in a graph are called edges. The degree of a vertex is equal to the number of edges that belong to it. The symbol we use to represent a complete graph with n vertices is nK. Next Worksheet Print Worksheet 1. What is a complete graph? A graph tha...
Let Em denote the set of edges of the complete graph on m vertices Km, and let f : Em → Em be a function. A subgraph G = (V (G), E (G)) of Km is called f-fixed if f(e) = e for all e ∈ E (G) and f-free if f(e) ∉ E(G) for all e ∈ E(G). For ...
The graph in Fig. 1 shows that the converse in general is not true. The reason for the choice of the term closed in Θn-closed is that we can use this notion to define a closure system, sensu [4], on the edges of the complete graph on V. As a mnemonic, the symbol Θ suggests...
Let f ( s, t; k ) be the largest value of m such that it is possible to k -color the edges of the complete graph K m so that every K s K m has exactly t colors occuring on its edges. The main object of this paper is to describe the behavior of the function f ( s , t...
There has been quite a bit of recent interest in a range of extremal problems involving counting the number of a given type of substructure in a graph. For instance, the number of independent sets or the number of the complete subgraphs1 of a graph. We let I(G) be the set of independ...
摘要: It is shown that the edges of the directed complete graph K n can be partitioned into edge disjoint directed 4-cycles if and only if 4 < n ≡ 0 or 1 (mod 4).关键词: Theoretical or Mathematical/ graph theory/ partition directed complete graph edge disjoint directed 4 cycles/ ...
A heterochromatic tree is an edge-colored tree in which any two edges have different colors. The heterochromatic tree partition number of an r -edge-colored graph G , denoted by t r ( G ), is the minimum positive integer p such that whenever the edges of the graph G are colored with ...
On the Decompositions of Complete Graphs into Cycles and Stars on the Same Number of Edges The notion of uniformity, as in uniform 1-factorisations, extends naturally to graph decompositions generally. The existence of uniform decompositions of c... A Abueida,C Lian - De Gruyter Open 被引量...
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-...