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- Kenneth P. Bogart, Peter C. Fishburn, Garth Isaak, Larry J. Langley
- Discrete Applied Mathematics
- 1995

We answer a question of Golumbic, Monma and Trotter by constructing proper tolerance graphs that are not unit tolerance graphs. An infinite family of graphs that are minimal in this respect is specified.

- David C. Fisher, Kathryn Fraughnaugh, Larry J. Langley, Douglas B. West
- J. Comb. Theory, Ser. B
- 1997

Let G be a graph with n nodes, e edges, chromatic number and girth g. In an acyclic orientation of G, an arc is dependent if its reversal creates a cycle. It is well known that if < g, then G has an acyclic orientation without dependent arcs. Edelman showed that if G is connected, then every acyclic orientation has at most e ? n + 1 dependent arcs. We show… (More)

- Larry J. Langley
- Discrete Applied Mathematics
- 1995

Recently, Hedetniemi et al. introduced (1, 2)-domination in graphs, and the authors extended that concept to (1, 2)-domination graphs of digraphs. Given vertices x and y in a digraph D, x and y form a (1, 2)-dominating pair if and only if for every other vertex z in D, z is one step away from x or y and at most two steps away from the other. The (1,… (More)

Competition graphs were rst introduced by Joel Cohen in the study of food webs and have since been extensively studied. Graphs which are the competition graph of a strongly connected or Hamiltonian digraph are of particular interest in applications to communication networks. It has been previously established that every graph without isolated vertices… (More)

- David C. Fisher, Kathryn Fraughnaugh, Larry J. Langley
- Ars Comb.
- 1997

- Kenneth P. Bogart, Michael S. Jacobson, Larry J. Langley, Fred R. McMorris
- Discrete Mathematics
- 2001

- David E. Brown, Larry J. Langley
- Australasian J. Combinatorics
- 2012

A graph is a probe interval graph (PIG) if its vertices can be partitioned into probes and nonprobes with an interval assigned to each vertex so that vertices are adjacent if and only if their corresponding intervals intersect and at least one of the vertices is a probe. When all intervals have the same length (or equivalently, no interval contains another… (More)

- Jason Albertson, Audene Harris, Larry J. Langley, Sarah K. Merz
- Ars Comb.
- 2006

- Kim A. S. Factor, Larry J. Langley
- Discrete Mathematics
- 2008

A domination graph of a digraph D, dom(D), is created using the vertex set of D and edge {u, v} ∈ E[dom(D)] whenever (u, z) ∈ A(D) or (v, z) ∈ A(D) for every other vertex z ∈ V (D). The underlying graph of a digraph D, UG(D), is the graph for which D is a biorientation. We completely characterize digraphs whose underlying graphs are identical to their… (More)