Robert E. Jamison

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We consider a generalization of edge intersection graphs of paths in a tree. Let P be a collection of nontrivial simple paths in a tree T . We define the k-edge (k 1) intersection graph k(P), whose vertices correspond to the members of P, and two vertices are joined by an edge if the corresponding members ofP share k edges in T . An undirected graphG is(More)
If V is a vector space over a finite field F, the minimum number of cosets of kdimensional subspaces of Vrequired to cover the nonzero points of V is established. This is done by first regarding V as a field extension of F and then associating with each coset L of a subspace of V a polynomial whose roots are the points of L. A covering with cosets is then(More)
A set K of nodes of a graph G is geodesically convex (respectively, monophonically convex) if K contains every node on every shortest (respectively, chordless) path joining nodes in K. We investigate the classes of graphs which are characterized by certain local convexity conditions with respect to geodesic convexity, in particular, those graphs in which(More)
The subchromatic number χS(G) of a graph G = (V,E) is the smallest order k of a partition {V1, V2, . . . , Vk} of the vertices V (G) such that the subgaph < Vi > induced by each subset Vi consisits of a disjoint union of complete subgraphs. By definition, χS(G) ≤ χ(G), the chromatic number of G. This paper develops properties of this lower bound for the(More)
A chordal graph is the intersection graph of a family of subtrees of a tree, or, equivalently, it is the (edge-)intersection graph of leaf-generated subtrees of a full binary tree. In this paper, a generalization of chordal graphs from this viewpoint is studied: a graph G=(V; E) is representable if there is a family of subtrees {Sv}v∈V of a binary tree,(More)
A chordal graph is the intersection graph of a family of subtrees of a host tree. In this paper we generalize this. A graph G = (V ,E) has an (h, s, t)-representation if there exists a host tree T of maximum degree at most h, and a family of subtrees {Sv}v∈V of T, all of maximum degree at most s, such that uv ∈ E if and only if |Su∩Sv | t . For given h, s,(More)