Multidesigns for Graph-Triples of Order 6
نویسندگان
چکیده
We call T = (G1, G2, G3) a graph-triple of order t if the Gi are pairwise non-isomorphic graphs on t non-isolated vertices whose edges can be combined to form Kt. If m ≥ t, we say T divides Km if E(Km) can be partitioned into copies of the graphs in T with each Gi used at least once, and we call such a partition a T -multidecomposition. In this paper, we study multidecompositions of Km for graph-triples of order 6. We focus on graph-triples in which either one graph is a perfect matching or all graphs have 5 edges each. Moreover, we determine maximum multipackings and minimum multicoverings when Km does not admit a multidecomposition.
منابع مشابه
Computing Szeged index of graphs on triples
ABSTRACT Let G=(V,E) be a simple connected graph with vertex set V and edge set E. The Szeged index of G is defined by where respectively is the number of vertices of G closer to u (respectively v) than v (respectively u). If S is a set of size let V be the set of all subsets of S of size 3. Then we define t...
متن کاملPotential forbidden triples implying hamiltonicity: for sufficiently large graphs
In [2], Brousek characterizes all triples of connected graphs, G1, G2, G3, with Gi = K1,3 for some i = 1, 2, or 3, such that all G1G2G3free graphs contain a hamiltonian cycle. In [8], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G1, G2, G3, none of which is a K1,s, s ≥ 3 such that G1G2G3-free graphs of sufficiently large order contain a hamiltonian cycl...
متن کاملMeasuring Accuracy of Triples in Knowledge Graphs
An increasing amount of large-scale knowledge graphs have been constructed in recent years. Those graphs are often created from text-based extraction, which could be very noisy. So far, cleaning knowledge graphs are often carried out by human experts and thus very inefficient. It is necessary to explore automatic methods for identifying and eliminating erroneous information. In order to achieve...
متن کاملForbidden triples implying Hamiltonicity: for all graphs
In [2], Brousek characterizes all triples of graphs, G1, G2, G3, with Gi = K1,3 for some i = 1, 2, or 3, such that all G1G2G3-free graphs contain a hamiltonian cycle. In [6], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G1, G2, G3, none of which is a K1,s, s ≥ 3 such that G1, G2, G3-free graphs of sufficiently large order contain a hamiltonian cycle. In...
متن کامل