Characterization of Unlabeled Level Planar Graphs

Fowler, J. Joseph; Kobourov, Stephen G.

doi:10.1007/978-3-540-77537-9_7

Cited by 16 publications

(34 citation statements)

References 14 publications

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“…The labelings in Fig. 9 of F ULP were shown to be level non-planar in [9,10]. In this section, we prove that of these, only the two trees, T 8 and T 9 , in T URLP are also radial level non-planar.…”

Section: Forbidden Unlabeled Radial Level Planar Graphsmentioning

confidence: 77%

“…3(a)-(g) [9,10] where any graph without a subdivision of one of these seven forbidden graphs is ULP. The class of ULP graphs consists of (i) generalized caterpillars (GCs) (formed by substituting edges of a caterpillar for ULP blocks as described in Fig.…”

Section: Related Previous Workmentioning

confidence: 99%

“…Hence, the drawing algorithms for ULP graphs given in [7,9,10] naturally extend to the radial setting. The drawing algorithm for generalized caterpillars detailed in [9,10] draws each ULP block proceeding left to right; see Fig. 6(a).…”

Section: Drawing Unlabeled Radial Level Planar Graphsmentioning

confidence: 99%

“…We can also directly extend the drawing algorithms from [7,9,10] for radius-2 stars and extended 3-spiders to give the next two lemmas, respectively. Next, we show how to realize the remaining two classes of URLP graphs in the subsequent two lemmas; the full proofs of each can be found in [8].…”

Section: Lemma 1 An N-vertex Generalized (Circular) Caterpillar Withmentioning

confidence: 99%

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Characterization of Unlabeled Radial Level Planar Graphs

Fowler

2010

Graph Drawing

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Abstract. Suppose that an n-vertex graph has a distinct labeling with the integers {1, . . . , n}. Such a graph is radial level planar if it admits a crossings-free drawing under two constraints. First, each vertex lies on a concentric circle such that the radius of the circle equals the label of the vertex. Second, each edge is drawn with a radially monotone curve. We characterize the set of unlabeled radial level planar (URLP) graphs that are radial level planar in terms of 7 and 15 forbidden subdivisions depending on whether the graph is disconnected or connected, respectively. We also provide linear-time drawing algorithms for any URLP graph.

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Section: Forbidden Unlabeled Radial Level Planar Graphsmentioning

confidence: 77%

Section: Related Previous Workmentioning

confidence: 99%

Section: Drawing Unlabeled Radial Level Planar Graphsmentioning

confidence: 99%

Section: Lemma 1 An N-vertex Generalized (Circular) Caterpillar Withmentioning

confidence: 99%

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Characterization of Unlabeled Radial Level Planar Graphs

Fowler

2010

Graph Drawing

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“…A complete characterization of ULP graphs has very recently been given in [12]. A planar graph is ULP if and only if it is either a generalized caterpillar, or a radius-2 star, or a generalized degree-3 spider.…”

Section: Theorem 3 a Planar Graph And An Ulp Graph Are Always Matchementioning

confidence: 99%

Matched Drawings of Planar Graphs

Giacomo¹,

Didimo²,

Kreveld³

et al. 2009

JGAA

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Abstract.A natural way to draw two planar graphs whose vertex sets are matched is to assign each matched pair a unique y-coordinate. In this paper we introduce the concept of such matched drawings, which are a relaxation of simultaneous geometric embeddings with mapping. We study which classes of graphs allow matched drawings and show that (i) two 3-connected planar graphs or a 3-connected planar graph and a tree may not be matched drawable, while (ii) two trees or a planar graph and a planar graph of some special families-such as unlabeled level planar (ULP) graphs or the family of "carousel graphs"-are always matched drawable.

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