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Papers by Beverly Jamison

Global Missiology English, Mar 4, 2015

Discrete Applied Mathematics, Jul 1, 1995

Studies in Applied Mathematics

A graph G is perfect in the sense of Berge if for every induced subgraph G′ of G, the chromatic n... more A graph G is perfect in the sense of Berge if for every induced subgraph G′ of G, the chromatic number χ(G′) equals the largest number ω(G′) of pairwise adjacent vertices in G′. The Strong Perfect Graph Conjecture asserts that a graph G is perfect if, and only if, neither G nor its complement Ḡ contains an odd chordless cycle of length at least five. We prove that the conjecture is true for a class of P5-free graphs.

The notions of binary string and binary symmetric function are introduced, and basic results pres... more The notions of binary string and binary symmetric function are introduced, and basic results presented. Boolean algorithms are given for binary addition and multiplication. An analysis of the redundancies involved is straightforward. The examination of carry propagation which arises in the Boolean analysis of functions may lead to a new interpretation of the notion of computational complexity.

P4-reducible graphs are precisely the graphs none of whose vertices belong to more than one chord... more P4-reducible graphs are precisely the graphs none of whose vertices belong to more than one chordless path with three edges. As it tarns out, the class of P4-reducible graphs strictly contains the well-known class of cographs. A remarkable property of Pa-reducible graphs is their unique tree representation up to isomorphism. In this paper we present a lineartime algorithm to recognize Pa-reducible graphs and to construct their corresponding tree representation.

SIAM Journal on Discrete Mathematics, 1995

ABSTRACT In this paper we introduce and investigate the notion of p-connectedness. As it turns ou... more ABSTRACT In this paper we introduce and investigate the notion of p-connectedness. As it turns out, this concept leads naturally to a unique tree representation for arbitrary graphs: the leaves of this tree are the p-connected components along with weak vertices, that is, vertices of the graph that belong to no p-connected component. We then show how to refine this decomposition to obtain a new decomposition that extends the well-known modular decomposition.

Siam Journal on Computing - SIAMCOMP, 1992

ABSTRACT A graph G is P 4 -sparse if no set of five vertices in G induces more than one chordless... more ABSTRACT A graph G is P 4 -sparse if no set of five vertices in G induces more than one chordless path of length three. P 4 -sparse graphs generalize both the class of cographs and the class of P 4 -reducible graphs. One remarkable feature of P 4 -sparse graphs is that they admit a tree representation unique up to isomorphism. It has been shown that this tree representation can be obtained in polynomial time. This paper gives a linear time algorithm to recognize P 4 -sparse graphs and shows how the data structures returned by the recognition algorithm can be used to construct the corresponding tree representation in linear time.

The Computer Journal - CJ, 1992

and , are any two states with transition probabilities Prob [<Kt + 1) = <*" 14(') = <U = 1 m. ... more and , are any two states with transition probabilities Prob [<Kt + 1) = <*" 14(') = <U = 1 m. "• then, P*((j> m) and P*U> n), the equilibrium probabilities of being in m and n respectively, obey:

Discrete Applied Mathematics, 1995

Discrete Applied Mathematics, 1991

Jamison, B. and S. Olariu, On a unique tree representation for P4-extendible graphs, Discrete App... more Jamison, B. and S. Olariu, On a unique tree representation for P4-extendible graphs, Discrete Applied Mathematics 34 (1991) 151-164. Several practical applications in computer science and computational linguistics suggest the study of graphs that are unlikely to have more than a few induced paths of length three. These applications have motivated the notion of a cograph, defined by the very strong restriction that no vertex may belong to an induced path of length three. The class of P,-extendible graphs that we introduce in this paper relaxes this restriction, and in fact properly contains the class of cographs, while still featuring the remarkable property of admitting a unique tree representation. Just as in the case of cographs, the class of P,-extendible graphs finds applications to clustering, scheduling, and memory management in a computer system. We give several characterizations for P4-extendible graphs and show that they can be constructed from single-vertex graphs by a finite sequence of operations. Our characterization implies that the P4-extendible graphs admit a tree representation unique up to isomorphism. Furthermore, this tree representation can be obtained in polynomial time.

Advances in Mathematics, 1975

Advances in Applied Mathematics, 1988