Ryan R. Martin

• Discrete Mathematics
• 2002
Let G be a tripartite graph with N vertices in each vertex class. If each vertex is adjacent to at least (2=3)N vertices in each of the other classes, then either G contains a subgraph that consistsâ€¦ (More)
• 9
• Discrete Mathematics
• 2008
Let G be a quadripartite graph with N vertices in each vertex class and each vertex is adjacent to at least (3/4)N vertices in each of the other classes. There exists an N0 such that, if N â‰¥ N0, thenâ€¦ (More)
• 8
• J. Comb. Theory, Ser. A
• 2013
The Boolean lattice of dimension two, also known as the diamond, consists of four distinct elements with the following property: A âŠ‚ B,C âŠ‚ D. A diamondfree family in the n-dimensional Boolean latticeâ€¦ (More)
• 6
• Random Struct. Algorithms
• 2003
This paper investigates the number of random edges required to add to an arbitrary dense graph in order to make the resulting graph hamiltonian with high probability. Adding (n) random edges is bothâ€¦ (More)
• 3
• Journal of Graph Theory
• 2008
An edge-operation on a graph G is defined to be either the deletion of an existing edge or the addition of a nonexisting edge. Given a family of graphs G, the editing distance from G to G is theâ€¦ (More)
• 3
• Discrete Mathematics
• 2012
In this paper, we discuss the induced saturation number. It is a nice generalization of the saturation number that will allow us to consider induced subgraphs. We define the induced saturationâ€¦ (More)
• 2
• Discrete Mathematics
• 2006
How many edges can a quadrilateral-free subgraph of a hypercube have? This question was raised by Paul ErdÅ‘s about 27 years ago. His conjecture that such a subgraph asymptotically has at most halfâ€¦ (More)
• 2
• Electr. J. Comb.
• 2008
In this paper, we provide a method for determining the asymptotic value of the maximum edit distance from a given hereditary property. This method permits the edit distance to be computed withoutâ€¦ (More)
• 2
• Discrete Mathematics
• 2007
In this paper we deal with codes identifying sets of vertices in random networks; that is, (1,â‰¤ l)-identifying codes. These codes enable us to detect sets of faulty processors in a multiprocessorâ€¦ (More)
• 1