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- W1412164264 abstract "This chapter describes the optimal embedding of a tree into an interval graph in linear time. The graphs considered in the chapter are finite, undirected, and simple. An interval supergraph for a given graph is called “optimal” if its clique number is smallest possible. The interval thickness θ(G) of a graph G is the minimum over the clique numbers of all interval graphs having a subgraph G. In the chapter, the following theorems are proved: (1) for any fixed integers k and d there is an algorithm deciding in time O(nk) for a given graph with maximal degree at most d, whether its interval thickness is at most k, and (2) For any integer k ≥ 2 and any tree T holds: θ(T) ≥ k + 1exists a node t V(T) with at least three branches Ttv, Ttu, Ttw at t such that θ(Ttv) ≥ k, θ(Ttu) ≥ k, θ(Ttw) ≥ k." @default.
- W1412164264 created "2016-06-24" @default.
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- W1412164264 date "1992-01-01" @default.
- W1412164264 modified "2023-10-18" @default.
- W1412164264 title "Optimal Embedding of a Tree into an Interval Graph in Linear Time" @default.
- W1412164264 cites W1980008391 @default.
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- W1412164264 doi "https://doi.org/10.1016/s0167-5060(08)70644-7" @default.
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