Add to ORKGA graph is a mathematical structure consisting of a set of objects called vertices and a set of 2-element subsets of vertices, called edges. The complete graph on n vertices is the graph with n vertices and an edge between any pair of distinct vertices. Let C6 denote the cycle on 6 vertices. We are interested in partitioning the edges of the complete graph on n vertices into copies of C6 and its complement with at least one copy of each graph. We provide necessary and sufficient conditions on n for the existence such a structure
AbstractLet G be a vertex-disjoint union of directed cycles in the complete directed graph Dt, let |...
Let G be a connected graph with p ≥ 2 vertices. For k = 1, 2, ..., P-1, the Kth order edge-connectiv...
AbstractIn this paper we use Tutte's f-factor theorem and the method of amalgamations to find necess...
We find both necessary and sufficient conditions for the existence of a (C6C overscore 6)-multidecom...
Firstly, a graph G consists of a vertex set V (G), and an edge set E (G) of endpoints which relate t...
Given two graphs G and H, a (G,H)-multidecomposition of Kn is a partition of the edges of Kn into co...
We call T = (G1, G2, G3) a graph-triple of order t if the Gi are pairwise non-isomorphic graphs on t...
AbstractA graph G is a common multiple of two graphs H1 and H2 if there exists a decomposition of G ...
A graph G is a common multiple of two graphs H-1 and H-2 if there exists a decomposition of G into e...
This paper surveys results on cycle decompositions of complete multipartite graphs (where the parts ...
AbstractValues of t, x, and m are obtained for which the complete multipartite graph defined by t in...
A directed graph is a way to encode information about directional relationships among objects. The c...
Let $M_v$ denotes a complete mixed graph on $v$ vertices, and let $S_6^i$ denotes the partial orient...
An H-decomposition of a graph G is a partition of the edges of G into subsets, each of which induces...
AbstractLet k, ℓ be positive integers. Let G be a graph of order kℓ. It is shown that if G is a comp...
AbstractLet G be a vertex-disjoint union of directed cycles in the complete directed graph Dt, let |...
Let G be a connected graph with p ≥ 2 vertices. For k = 1, 2, ..., P-1, the Kth order edge-connectiv...
AbstractIn this paper we use Tutte's f-factor theorem and the method of amalgamations to find necess...
We find both necessary and sufficient conditions for the existence of a (C6C overscore 6)-multidecom...
Firstly, a graph G consists of a vertex set V (G), and an edge set E (G) of endpoints which relate t...
Given two graphs G and H, a (G,H)-multidecomposition of Kn is a partition of the edges of Kn into co...
We call T = (G1, G2, G3) a graph-triple of order t if the Gi are pairwise non-isomorphic graphs on t...
AbstractA graph G is a common multiple of two graphs H1 and H2 if there exists a decomposition of G ...
A graph G is a common multiple of two graphs H-1 and H-2 if there exists a decomposition of G into e...
This paper surveys results on cycle decompositions of complete multipartite graphs (where the parts ...
AbstractValues of t, x, and m are obtained for which the complete multipartite graph defined by t in...
A directed graph is a way to encode information about directional relationships among objects. The c...
Let $M_v$ denotes a complete mixed graph on $v$ vertices, and let $S_6^i$ denotes the partial orient...
An H-decomposition of a graph G is a partition of the edges of G into subsets, each of which induces...
AbstractLet k, ℓ be positive integers. Let G be a graph of order kℓ. It is shown that if G is a comp...
AbstractLet G be a vertex-disjoint union of directed cycles in the complete directed graph Dt, let |...
Let G be a connected graph with p ≥ 2 vertices. For k = 1, 2, ..., P-1, the Kth order edge-connectiv...
AbstractIn this paper we use Tutte's f-factor theorem and the method of amalgamations to find necess...