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Characterizing forbidden pairs for hamiltonian properties
TLDR
We characterize those pairs of forbidden subgraphs sufficient to imply various hamiltonian type properties in graphs and present a result concerning the pairs for such graphs. 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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Graphs with prescribed degree sets and girth
For a finite nonempty set of integers, each of which is at least two, and an integern ≥ 3, the numberf(;n) is defined as the least order of a graph having degree set and girthn. The numberf(;n) isExpand
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Saturation numbers for families of Ramsey-minimal graphs
Given a family of graphs F , a graph G is F-saturated if no element of F is a subgraph of G, but for any edge e in G, some element of F is a subgraph of G + e. Let sat(n,F) denote the minimum numberExpand
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Extremal Graphs for Intersecting Triangles
TLDR
In this paper, we determine the minimum number of edges sufficient for the existence of k triangles intersecting in exactly one common vertex. Expand
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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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Advances on the Hamiltonian Problem – A Survey
  • R. Gould
  • Mathematics, Computer Science
  • Graphs Comb.
  • 1 March 2003
TLDR
The hamiltonian problem is generally considered to be determining conditions under which a graph contains a spanning cycle. Expand
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Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size
TLDR
A graph $G$ is said to be F -saturated if G contains no copy of F as a subgraph, but for any edge in the complement of $G$, the graph does contain a cycle of length $l$. Expand
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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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On H-Linked Graphs
TLDR
We say a graph G is H-linked if for every choice of k vertices v1, . . . , vk in G, there exists a subdivision of H in G such that vi represents hi (for all i). Expand
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