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- W2247177778 abstract "The main purpose of this thesis is to study three problems concerning extremal graphs. The first is the problem of finding a minimal 2-edge connected subgraph of a 2-edge connected graph, the second is the problem of finding a minimal 2-connected subgraph of a 2-connected graph, and the third is the problem of finding a maximal planar subgraph of a nonplanar graph. These problems have useful applications in computer network and electronic circuit design.This thesis is divided into five chapters.In the first chapter, we discuss the theory of extremal graphs and graph algorithm design in general.In the second chapter, we present an efficient algorithm for the problem of finding a minimal 2-edge connected subgraph of a 2-edge connected graph. The algorithm takes O($m + n$) time and O($m + n$) space.In the third chapter, we present an efficient algorithm for the problem of finding a minimal 2-connected subgraph of a 2-connected graph. The algorithm in chapter three also takes O($m + n$) time and ($m + n$) space.In the fourth chapter, we discuss an algorithm for the problem of finding a maximal planar subgraph of a nonplanar graph. The algorithm runs in O($mcdot log$(n)) time and O($m + n$) space.The fifth chapter discusses a parallel algorithm for transitively orienting comparability graphs. The algorithm has many applications in designing parallel algorithms for such special perfect graphs as chordal graphs, permutation graphs and comparability graphs." @default.
- W2247177778 created "2016-06-24" @default.
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- W2247177778 date "1991-05-01" @default.
- W2247177778 modified "2023-09-27" @default.
- W2247177778 title "An algorithmic approach to extremal graph problems" @default.
- W2247177778 hasPublicationYear "1991" @default.
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