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Dominating Sets for Outerplanar Graphs
"... Abstract: We provide lower and upper bounds for the domination numbers and the connected domination numbers for outerplanar graphs. We also provide a recursive algorithm that finds a connected domination set for an outerplanar graph. Finally, we show that for outerplanar graphs where all bounded fa ..."
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Abstract: We provide lower and upper bounds for the domination numbers and the connected domination numbers for outerplanar graphs. We also provide a recursive algorithm that finds a connected domination set for an outerplanar graph. Finally, we show that for outerplanar graphs where all bounded
Generating Random Outerplanar Graphs
 In 1 st Workshop on Algorithms for Listing, Counting, and Enumeration
, 2003
"... We show how to generate labeled and unlabeled outerplanar graphs with n vertices uniformly at random in (expected) polynomial time in n. To generate these graphs, we present a new counting technique using the decomposition of a graph according to its block structure and compute the exact number ..."
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Cited by 5 (2 self)
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We show how to generate labeled and unlabeled outerplanar graphs with n vertices uniformly at random in (expected) polynomial time in n. To generate these graphs, we present a new counting technique using the decomposition of a graph according to its block structure and compute the exact number
Generating Outerplanar Graphs
"... supported by the DFG (GRK 588/1) Abstract. We show how to generate labeled and unlabeled outerplanar graphs with n vertices uniformly at random in polynomial time in n. To generate labeled outerplanar graphs, we present a counting technique using the decomposition of a graph according to its block s ..."
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supported by the DFG (GRK 588/1) Abstract. We show how to generate labeled and unlabeled outerplanar graphs with n vertices uniformly at random in polynomial time in n. To generate labeled outerplanar graphs, we present a counting technique using the decomposition of a graph according to its block
Enumeration of Unlabeled Outerplanar Graphs
"... We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number gn of unlabeled outerplanar graphs on n vertices can be computed in polynomial time, and gn is asymptotically g n −5/2 ρ −n, where g≈0.00909941 and ρ −1 ≈ 7.50360 can be approximated. Using our enumerative ..."
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Cited by 4 (1 self)
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We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number gn of unlabeled outerplanar graphs on n vertices can be computed in polynomial time, and gn is asymptotically g n −5/2 ρ −n, where g≈0.00909941 and ρ −1 ≈ 7.50360 can be approximated. Using our
On colorings of squares of outerplanar graphs
 Proceedings of the Fifteenth Annual ACMSIAM Symposium on Discrete Algorithms
, 2004
"... We study vertex colorings of the square G 2 of an outerplanar graph G. We find the optimal bound of the inductiveness, chromatic number and the clique number of G 2 as a function of the maximum degree ∆ of G for all ∆ ∈ N. As a bonus, we obtain the optimal bound of the choosability (or the listchr ..."
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Cited by 10 (2 self)
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We study vertex colorings of the square G 2 of an outerplanar graph G. We find the optimal bound of the inductiveness, chromatic number and the clique number of G 2 as a function of the maximum degree ∆ of G for all ∆ ∈ N. As a bonus, we obtain the optimal bound of the choosability (or the list
Pathwidth of Outerplanar Graphs
 Journal of Graph Theory
, 2007
"... We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [3], after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual ..."
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Cited by 5 (2 self)
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We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [3], after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual
Vertex Degrees in Outerplanar Graphs
, 2010
"... n−6 k−4 For an outerplanar graph on n vertices, we determine the maximum number of vertices of degree at least ⌊ k. For ⌋ k = 4 (and n ≥ 7) the answer is n −4. For k = 5 (and ..."
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n−6 k−4 For an outerplanar graph on n vertices, we determine the maximum number of vertices of degree at least ⌊ k. For ⌋ k = 4 (and n ≥ 7) the answer is n −4. For k = 5 (and
On the orthogonal drawing of outerplanar graphs
 in Proceedings of COCOON ’04, Lect. Notes Comput. Sci. 3106
, 2004
"... Abstract. In this paper we show that an outerplanar graph G with maximum degree at most 3 has a 2D orthogonal drawing with no bends if and only if G contains no triangles. We also show that an outerplanar graph G with maximum degree at most 6 has a 3D orthogonal drawing with no bends if and only i ..."
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Cited by 5 (1 self)
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Abstract. In this paper we show that an outerplanar graph G with maximum degree at most 3 has a 2D orthogonal drawing with no bends if and only if G contains no triangles. We also show that an outerplanar graph G with maximum degree at most 6 has a 3D orthogonal drawing with no bends if and only
Proximity Drawings of Outerplanar Graphs
, 1996
"... A proximity drawing of a graph is one in which pairs of adjacent vertices are drawn relatively close together according to some proximity measure while pairs of nonadjacent vertices are drawn relatively far apart. The fundamental question concerning proximity drawability is: Given a graph G and a d ..."
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Cited by 13 (6 self)
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definition of proximity, is it possible to construct a proximity drawing of G? We consider this question for outerplanar graphs with respect to an infinite family of proximity drawings called fidrawings. These drawings include as special cases the wellknown Gabriel drawings (when fi = 1), and relative
On Infinite Generalized Outerplanar Graphs
"... Sedl'acek in [6] defined the generalized outerplanar graphs like the finite graphs which can be embedded in the plane in such a way that at least one endvertex of each edge lies on the boundary of the same face, and he gave a characterization of them by forbidden subgraphs. In this paper, we s ..."
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Sedl'acek in [6] defined the generalized outerplanar graphs like the finite graphs which can be embedded in the plane in such a way that at least one endvertex of each edge lies on the boundary of the same face, and he gave a characterization of them by forbidden subgraphs. In this paper, we
Results 1  10
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