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133
personal communication
, 1994
"... We study HananiTutte style theorems for various notions of planarity, including partially embedded planarity and simultaneous planarity. This approach brings together the combinatorial, computational and algebraic aspects of planarity notions and may serve as a uniform foundation for planarity, as ..."
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Cited by 14 (0 self)
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We study HananiTutte style theorems for various notions of planarity, including partially embedded planarity and simultaneous planarity. This approach brings together the combinatorial, computational and algebraic aspects of planarity notions and may serve as a uniform foundation for planarity, as suggested earlier in the writings of Tutte and Wu. Submitted:
Matched Drawings of Planar Graphs
, 2007
"... A natural way to draw two planar graphs whose vertex sets are matched is to assign each matched pair a unique ycoordinate. 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 all ..."
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Cited by 7 (3 self)
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A natural way to draw two planar graphs whose vertex sets are matched is to assign each matched pair a unique ycoordinate. 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 3connected planar graphs or a 3connected 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.
On maximum differential graph coloring
 In 18th Symp. on Graph Drawing (GD
, 2010
"... Abstract. We study the maximum differential graph coloring problem, in which the goal is to find a vertex labeling for a given undirected graph that maximizes the label difference along the edges. This problem has its origin in map coloring, where not all countries are necessarily contiguous. We def ..."
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Cited by 9 (6 self)
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Abstract. We study the maximum differential graph coloring problem, in which the goal is to find a vertex labeling for a given undirected graph that maximizes the label difference along the edges. This problem has its origin in map coloring, where not all countries are necessarily contiguous. We define the differential chromatic number and establish the equivalence of the maximum differential coloring problem to that of kHamiltonian path. As computing the maximum differential coloring is NPComplete, we describe an exact backtracking algorithm and a spectralbased heuristic. We also discuss lower bounds and upper bounds for the differential chromatic number for several classes of graphs. 1
A SIMULATIONBASED APPROACH FOR ESTIMATING THE COMMERCIAL CAPACITY OF RAILWAYS
"... Rail transport is expected to play a remarkable role for a sustainable mobility in Europe. This paper presents an approach for estimating the commercial capacity of railways. The commercial capacity is intended as the number of possible paths in a defined time window on a rail line, or part of it, ..."
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Rail transport is expected to play a remarkable role for a sustainable mobility in Europe. This paper presents an approach for estimating the commercial capacity of railways. The commercial capacity is intended as the number of possible paths in a defined time window on a rail line, or part of it, considering a fixed path mix, with marketoriented quality. The capacity management is one of the most important tasks of railway Infrastructure Managers. The proposed simulationbased approach relies on the use of an optimizer and a simulator. The study has been developed for the rail line Verona–Brennero, located in the Italian part of the European Corridor Hamburg–Napoli. Computational results allowed to estimate the commercial capacity differences between the whole line and three important line sections within it. Other computational experiments showed the relevant estimated increase in commercial capacity that a reduction in time spacing between trains could imply. 1
Drawing colored graphs on colored points
, 2006
"... Let G be a planar graph with n vertices whose vertex set is partitioned into subsets V0,..., Vk−1 for some positive integer 1 ≤ k ≤ n and let S be a set of n distinct points in the plane partitioned into subsets S0,..., Sk−1 with Vi  = Si  (0 ≤ i ≤ k − 1). This paper studies the problem of comp ..."
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Cited by 10 (3 self)
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Let G be a planar graph with n vertices whose vertex set is partitioned into subsets V0,..., Vk−1 for some positive integer 1 ≤ k ≤ n and let S be a set of n distinct points in the plane partitioned into subsets S0,..., Sk−1 with Vi  = Si  (0 ≤ i ≤ k − 1). This paper studies the problem of computing a crossingfree drawing of G such that each vertex of Vi is mapped to a distinct point of Si. Lower and upper bounds on the number of bends per edge are proved for any 2 ≤ k ≤ n. As a special case, we improve the upper and lower bounds presented in a paper by Pach and Wenger for k = n [Graphs and Combinatorics (2001), 17:717–728].
Constrained Simultaneous and Nearsimultaneous Embeddings
, 2007
"... A geometric simultaneous embedding of two graphs G1 = (V1, E1) and G2 = (V2, E2) with a bijective mapping of their vertex sets γ: V1 → V2 is a pair of planar straightline drawings Γ1 of G1 and Γ2 of G2, such that each vertex v2 = γ(v1) is mapped in Γ2 to the same point where v1 is mapped in Γ1, wh ..."
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Cited by 9 (3 self)
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A geometric simultaneous embedding of two graphs G1 = (V1, E1) and G2 = (V2, E2) with a bijective mapping of their vertex sets γ: V1 → V2 is a pair of planar straightline drawings Γ1 of G1 and Γ2 of G2, such that each vertex v2 = γ(v1) is mapped in Γ2 to the same point where v1 is mapped in Γ1, where v1 ∈ V1 and v2 ∈ V2. In this paper we examine several constrained versions and a relaxed version of the geometric simultaneous embedding problem. We show that if the input graphs are assumed to share no common edges this does not seem to yield large classes of graphs that can be simultaneously embedded. Further, if a prescribed combinatorial embedding for each input graph must be preserved, then we can answer some of the problems that are still open for geometric simultaneous embedding. Finally, we present some positive and negative results on the nearsimultaneous embedding problem, in which vertices are not forced to be placed exactly in the same, but just in “near” points in different drawings.
Results 11  20
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