Results 1  10
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14
A linear time algorithm for embedding graphs in an arbitrary surface
 SIAM J. Discrete Math
, 1999
"... Ljubljana, February 2, 2009A simpler linear time algorithm for embedding graphs into an arbitrary surface and the genus of graphs of bounded treewidth ..."
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Cited by 56 (10 self)
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Ljubljana, February 2, 2009A simpler linear time algorithm for embedding graphs into an arbitrary surface and the genus of graphs of bounded treewidth
Planarization of Graphs Embedded on Surfaces
 in WG
, 1995
"... A planarizing set of a graph is a set of edges or vertices whose removal leaves a planar graph. It is shown that, if G is an nvertex graph of maximum degree d and orientable genus g, then there exists a planarizing set of O( p dgn) edges. This result is tight within a constant factor. Similar res ..."
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Cited by 7 (1 self)
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A planarizing set of a graph is a set of edges or vertices whose removal leaves a planar graph. It is shown that, if G is an nvertex graph of maximum degree d and orientable genus g, then there exists a planarizing set of O( p dgn) edges. This result is tight within a constant factor. Similar results are obtained for planarizing vertex sets and for graphs embedded on nonorientable surfaces. Planarizing edge and vertex sets can be found in O(n + g) time, if an embedding of G on a surface of genus g is given. We also construct an approximation algorithm that finds an O( p gn log g) planarizing vertex set of G in O(n log g) time if no genusg embedding is given as an input. 1 Introduction A graph G is planar if G can be drawn in the plane so that no two edges intersect. Planar graphs arise naturally in many applications of graph theory, e.g. in VLSI and circuit design, in network design and analysis, in computer graphics, and is one of the most intensively studied class of graphs [2...
Bounded Combinatorial Width and Forbidden Substructures
, 1995
"... All rights reserved. This dissertation may not be reproduced in whole or in part, by mimeograph or other means, without the permission of the author. Supervisor: M. R. Fellows A substantial part of the history of graph theory deals with the study and classication of sets of graphs that share common ..."
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Cited by 4 (2 self)
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All rights reserved. This dissertation may not be reproduced in whole or in part, by mimeograph or other means, without the permission of the author. Supervisor: M. R. Fellows A substantial part of the history of graph theory deals with the study and classication of sets of graphs that share common properties. One predominant trend is to characterize graph families by sets of minimal forbidden graphs (within some partial ordering on the graphs). For example, the famous Kuratowski Theorem classi es the planar graph family by two forbidden graphs (in the topological partial order). Most, if not all, of the current approaches for nding these forbidden substructure characterizations use extensive and specialized case analysis. Thus, until now, for a xed graph family,thistype of mathematical theorem proving often required months or even years of human e ort. The main focus of this dissertation is to develop a practical theory for automating (with distributed computer programming) this classic part of graph theory. We extend and (more importantly) implement avariation
Embeddings of cubic halin graphs: a surfacebysurface inventory
 Ars Mathematica Contemporanea
"... We derive an O(n2)time algorithm for calculating the sequence of numbers g0(G), g1(G), g2(G),... of distinct ways to embed a 3regular Halin graph G on the respective orientable surfaces S0, S1, S2,.... Key topological features are a quadrangular decomposition of plane Halin graphs and a new recomb ..."
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Cited by 3 (3 self)
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We derive an O(n2)time algorithm for calculating the sequence of numbers g0(G), g1(G), g2(G),... of distinct ways to embed a 3regular Halin graph G on the respective orientable surfaces S0, S1, S2,.... Key topological features are a quadrangular decomposition of plane Halin graphs and a new recombinantstrands reassembly process that fits pieces together threeatavertex. Key algorithmic features are reassembly along a postorder traversal, with justintime dynamic assignment of roots for quadrangular pieces encountered along the tour. 1.
Too many minor order obstructions (for parametrized lower ideals
 Journal of Universal Computer Science
, 1997
"... Abstract: We study the growth rate on the number obstructions (forbidden minors) for families of graphs that are based on parameterized graph problems. Our main result shows that if the de ning graph problem is NPcomplete then the growth rate on the number of obstructions must be superpolynomial o ..."
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Cited by 2 (1 self)
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Abstract: We study the growth rate on the number obstructions (forbidden minors) for families of graphs that are based on parameterized graph problems. Our main result shows that if the de ning graph problem is NPcomplete then the growth rate on the number of obstructions must be superpolynomial or else the polynomialtime P hierarchy must collapse to 3.We illustrate the rapid growth rate of parameterized lower ideals by computing (and counting) the obstructions for the graph families with independence plus size at most k, k 12. Key Words: graph minors, obstruction sets, polynomial hierarchy Category: F.4, F.m, G.2
A Map Colour Theorem for the Union of Graphs
, 2003
"... In 1890 Heawood [10] established an upper bound for the chromatic number of a graph embedded on a surface of Euler genus g 1. ..."
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Cited by 2 (0 self)
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In 1890 Heawood [10] established an upper bound for the chromatic number of a graph embedded on a surface of Euler genus g 1.
Topological Graph Theory  A Survey
 Cong. Num
, 1996
"... this paper we give a survey of the topics and results in topological graph theory. We offer neither breadth, as there are numerous areas left unexamined, nor depth, as no area is completely explored. Nevertheless, we do offer some of the favorite topics of the author and attempt to place them 1 ..."
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Cited by 1 (0 self)
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this paper we give a survey of the topics and results in topological graph theory. We offer neither breadth, as there are numerous areas left unexamined, nor depth, as no area is completely explored. Nevertheless, we do offer some of the favorite topics of the author and attempt to place them 1
CLASSIFICATION OF RINGS WITH GENUS ONE ZERODIVISOR GRAPHS
"... Abstract. This paper investigates properties of the zerodivisor graph of a commutative ring and its genus. In particular, we determine all isomorphism classes of finite commutative rings with identity whose zerodivisor graph has genus 1. 1. ..."
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Abstract. This paper investigates properties of the zerodivisor graph of a commutative ring and its genus. In particular, we determine all isomorphism classes of finite commutative rings with identity whose zerodivisor graph has genus 1. 1.
Topological Graph Theory from Japan
"... This is a survey of studies on topological graph theory developed by Japanese people in the recent two decades and presents a big bibliography including almost all papers written by Japanese topological graph theorists. ..."
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Cited by 1 (0 self)
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This is a survey of studies on topological graph theory developed by Japanese people in the recent two decades and presents a big bibliography including almost all papers written by Japanese topological graph theorists.
Asymptotic enumeration of labelled graphs by genus
"... We obtain asymptotic formulas for the number of rooted 2connected and 3connected surface maps on an orientable surface of genus g with respect to vertices and edges simultaneously. We also derive the bivariate version of the large facewidth result for random 3connected maps. These results are the ..."
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We obtain asymptotic formulas for the number of rooted 2connected and 3connected surface maps on an orientable surface of genus g with respect to vertices and edges simultaneously. We also derive the bivariate version of the large facewidth result for random 3connected maps. These results are then used to derive asymptotic formulas for the number of labelled kconnected graphs of orientable genus g for k ≤ 3. 1