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- W2911444009 abstract "In a Open image in new window -contact representation of a planar graph G, each vertex is represented as an axis-aligned plus shape consisting of two intersecting line segments (or equivalently, four axis-aligned line segments that share a common endpoint), and two plus shapes touch if and only if their corresponding vertices are adjacent in G. Let the four line segments of a plus shape be its arms. In a c-balanced representation, c ≤ 1, every arm can touch at most (lceil cvarDeltarceil) other arms, where (varDelta) is the maximum degree of G. The widely studied T- and L-contact representations are c-balanced representations, where c could be as large as 1. In contrast, the goal in a c-balanced representation is to minimize c. Let c k , where k ∈ {2,3}, be the smallest c such that every planar k-tree has a c-balanced representation. In this paper we show that 1/4 ≤ c 2 ≤ 1/3 ( = b 2) and 1/3 < c 3 ≤ 1/2 ( = b 3). Our result has several consequences. Firstly, planar k-trees admit 1-bend box-orthogonal drawings with boxes of size (lceil b_kvarDeltarceil times lceil b_kvarDeltarceil), which generalizes a result of Tayu, Nomura, and Ueno. Secondly, they admit 1-bend polyline drawings with (2lceil b_kvarDeltarceil) slopes, which is significantly smaller than the (2varDelta) upper bound established by Keszegh, Pach, and Palvolgyi for arbitrary planar graphs." @default.
- W2911444009 created "2019-02-21" @default.
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- W2911444009 date "2013-09-23" @default.
- W2911444009 modified "2023-09-23" @default.
- W2911444009 title "On Balanced Open image in new window-Contact Representations" @default.
- W2911444009 hasPublicationYear "2013" @default.
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