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n-Domination in graphs
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The bondage number of a graph
TLDR
We define the bondage number of a graph G to be the cardinality of a smallest set E of edges for which σ(G−E)>σ(G). Expand
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Neighborhood unions and hamiltonian properties in graphs
TLDR
We investigate the relationship between the cardinality of the union of the neighborhoods of an arbitrary pair of nonadjacent vertices and various hamiltonian type properties in graphs. We show that if G is 2-connected, of order p ≥ 3 and if N(x) ⌣ N(y)∥ ≧ (p − 1)2, then G is traceable. Expand
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On graphs having domination number half their order
In this paper we present a characterization of connected graphs of order 2n with domination numbern. Using this class of graphs, we determine an infinite class of graphs with the property that theExpand
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Edge disjoint monochromatic triangles in 2-colored graphs
TLDR
Minimum number of pairwise edge disjoint monochromatic complete graphs K k in any 2-coloring of the edges of a K n . Expand
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Characterizing degree-sum maximal nonhamiltonian bipartite graphs
TLDR
In 1963, Moon and Moser gave a bipartite analogue to Ore's famed theorem on hamiltonian graphs, consisting of one infinite family and two exceptional graphs of order eight. Expand
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Graph Saturation in Multipartite Graphs
Let $G$ be a fixed graph and let ${\mathcal F}$ be a family of graphs. A subgraph $J$ of $G$ is ${\mathcal F}$-saturated if no member of ${\mathcal F}$ is a subgraph of $J$, but for any edge $e$ inExpand
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On n-domination, n-dependence and forbidden subgraphs
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Ramsey numbers in rainbow triangle free colorings
TLDR
We consider the problem of finding the minimum number n such that any k edge colored complete graph on n vertices contains either a three colored triangle or a monochromatic copy of the graph G. Expand
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A Note on Graphs Which Have Upper Irredundance Equal to Independence
TLDR
We introduce the concept of a graph G being irredundant perfect if IR ( H )= β ( H) for all induced subgraphs H of G . Expand
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