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- Csaba Magyar, 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)

- Ryan R. Martin, Endre SzemerÃ©di
- 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)

- Lucas Kramer, Ryan R. Martin, Michael Young
- 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)

- Tom Bohman, Alan M. Frieze, Ryan R. Martin
- 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)

- Maria Axenovich, AndrÃ© E. KÃ©zdy, Ryan R. Martin
- 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)

- Alan M. Frieze, Michael Krivelevich, Ryan R. Martin
- Random Struct. Algorithms
- 2004

- Ryan R. Martin, Jason J. Smith
- 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)

- Maria Axenovich, Ryan R. Martin
- 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)

- JÃ³zsef Balogh, Ryan R. Martin
- 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)

- Alan M. Frieze, Ryan R. Martin, Julien Moncel, MiklÃ³s RuszinkÃ³, Clifford D. Smyth
- 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)