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Structure and Recognition of Graphs with No 6-wheel Subdivision

Rebecca Robinson, Graham Farr
2008 Algorithmica  
ÓÖ v 0 v 0 v 0 Structure and recognition of graphs with no 6-wheel subdivision Rebecca Robinson Characterization of graphs that do not contain a W 6 -subdivision Theorem.  ...  of graphs with no 6-wheel subdivision Rebecca Robinson  ... 
doi:10.1007/s00453-007-9162-y fatcat:nbbbxru4nzb4rhpwgak2wdzcfy

Page 4567 of Mathematical Reviews Vol. , Issue 96h [page]

1996 Mathematical Reviews  
Random Structures Algorithms 6 (1995), no. 2-3, 331-340.  ...  Random Structures Algorithms 6 (1995), no. 2-3, 323-329.  ... 

Clique‐cutsets beyond chordal graphs

Valerio Boncompagni, Irena Penev, Kristina Vušković
2018 Journal of Graph Theory  
In this paper, we study the structure of graphs that contain (as induced subgraphs) no Truemper configurations other than (possibly) universal wheels and twin wheels.  ...  Truemper configurations (thetas, pyramids, prisms, and wheels) have played an important role in the study of complex hereditary graph classes (e.g. the class of perfect graphs and the class of even-hole-free  ...  A theta is any subdivision of the complete bipartite graph K 2,3 .Apyramid is any subdivision of the complete graph K 4 in which one triangle remains unsubdivided, and of the remaining three edges, at  ... 
doi:10.1002/jgt.22428 fatcat:3op75pg36zbo7a6572uys5v6ra

Search strategies for developing characterizations of graphs without small wheel subdivisions [article]

Rebecca Robinson, Graham Farr
2013 arXiv   pre-print
Proving a result for the wheel with six spokes requires extensive case analysis on many small graphs, and even more such analysis is needed for the wheel with seven spokes.  ...  Practical algorithms for solving the Subgraph Homeomorphism Problem are known for only a few small pattern graphs: among these are the wheel graphs with four, five, six, and seven spokes.  ...  Structure and recognition of graphs with no 6-wheel subdivision. Published online in Algorithmica, January 2008; awaiting print publication. [6] Rebecca Robinson and Graham Farr.  ... 
arXiv:1311.0574v1 fatcat:wn2ud2l6cnfpflzufhd3bkjolm

On graphs with no induced subdivision of K4

Benjamin Lévêque, Frédéric Maffray, Nicolas Trotignon
2012 Journal of combinatorial theory. Series B (Print)  
We obtain also a structure theorem for the class C of graphs that contain neither a subdivision of K_4 nor a wheel as an induced subgraph, where a wheel is a cycle on at least four vertices together with  ...  Our structure theorem is used to prove that every graph in C is 3-colorable and entails a polynomial-time recognition algorithm for membership in C.  ...  Acknowledgment We are grateful to Alex Scott for showing us the proof of Theorem 1.6.  ... 
doi:10.1016/j.jctb.2012.04.005 fatcat:377entngsfd3xalcm5wq5hw3o4

On the reconstruction of planar graphs

Mark Bilinski, Young Soo Kwon, Xingxing Yu
2007 Journal of combinatorial theory. Series B (Print)  
We show that the planarity of a graph can be recognized from its vertex deleted subgraphs, which answers a question posed by Bondy and Hemminger in 1979.  ...  We also state some useful counting lemmas and use them to reconstruct certain planar graphs.  ...  In particular, we thank the referee who pointed out that Lemmas 2.1 and 2.2 for n = 2 are given in [13] .  ... 
doi:10.1016/j.jctb.2006.12.005 fatcat:vzciptefoze6lfkdtfsonsytdq

The existence of homeomorphic subgraphs in chordal graphs

C.R. Subramanian, C.E. Veni Madhavan
1997 Applied Mathematics Letters  
We establish conditions for the existence, in a chordal graph, of subgraphs homeomorphic to Kn (n >_ 3), Km,n (m, n >_ 2), and wheels Wr (r _> 3).  ...  Using these results, we develop a simple linear time algorithm for testing planarity of chordal graphs.  ...  Farr [5] gives characterizations of general graphs having no subgraphs homeomorphic to wheels W4 and Ws.  ... 
doi:10.1016/s0893-9659(97)00027-x fatcat:q4663fbr2vdzhkgsbj3u73gfoq

Even-hole-free graphs: A survey

Vuskovic Kristina
2010 Applicable Analysis and Discrete Mathematics  
Graph Conjecture and their polynomial time recognition.  ...  The class of even-hole-free graphs is structurally quite similar to the class of perfect graphs, which was the key initial motivation for their study.  ...  Similarly when one works with odd-hole-free graphs one relies on odd wheels and 3P C(Δ, ·)'s as excluded structures.  ... 
doi:10.2298/aadm100812027v fatcat:f4bhcsqbc5hrpl5zifpxxoi3fm

Fan-Crossing Free Graphs and Their Relationship to other Beyond-Planar Graphs [article]

Franz J. Brandenburg
2020 arXiv   pre-print
In particular, we show that the 2-subdivision and the node-to-circle expansion of any graph is fan-crossing free, which does not hold for fan-crossing and k-(gap)-planar graphs, respectively.  ...  We use the subdivision, node-to-circle expansion and path-addition operations to distinguish all these graph classes.  ...  An extended wheel graph XW 2k consists of two poles p and q and a circle of length 2k. There is an edge between each pole and each vertex of the circle, whereas there is no edge pq.  ... 
arXiv:2003.08468v2 fatcat:diek3q7zd5hmtklr22zpkr6wqe

Detecting induced subdivision of K_4 [article]

Ngoc Khang Le
2017 arXiv   pre-print
In this paper, we propose a polynomial-time algorithm to test whether a given graph contains a subdivision of K_4 as an induced subgraph.  ...  Acknowledgement The author would like to thank Nicolas Trotignon for his help and useful discussion.  ...  For a fixed graph H, the question of detecting induced subdivision of H in a given graph has been studied in [6] .  ... 
arXiv:1703.04637v1 fatcat:e3e5vc5zybgjbp74carh7kwnim

Structure of classes of graphs defined by forbidding induced subgraphs [article]

Nicolas Trotignon
2013 arXiv   pre-print
This document is the Habilitation Thesis (Habilitation \'a Diriger des Recherches) of Nicolas Trotignon. It presents his work in structural graph theory, from 2001 to 2009.  ...  So, a line-graph with no wheel is the line-graph of a chordless graph.  ...  Induced subdivision of K 4 Graphs with no subdivision of K 4 as a possibly non-induced subgraph are called series-parallel graphs. The structure of series-parallel graphs is wellknown.  ... 
arXiv:1308.6678v1 fatcat:xgtoz7wi5nd7df3efa3lanoidq

Detecting wheels

Emilie Diot, Sébastien Tavenas, Nicolas Trotignon
2014 Applicable Analysis and Discrete Mathematics  
A wheel is a graph made of a cycle of length at least 4 together with a vertex that has at least three neighbors in the cycle.  ...  We prove that the problem whose instance is a graph G and whose question is "does G contains a wheel as an induced subgraph" is NP-complete. We also settle the complexity of several similar problems.  ...  Hence, the algorithm can be implemented to run in time O(n 4 ). 2 Theorem 3.6 and its proof suggest that graphs with no wheels and no complement of wheels form a restricted class that might have a simple  ... 
doi:10.2298/aadm131128023d fatcat:ydgzkuf7ljbpxkocycqomvrezu

Hexahedral Mesh Generation using the Embedded Voronoi Graph

A. Sheffer, M. Etzion, A. Rappoport, M. Bercovier
1999 Engineering with Computers  
The embedded Voronoi graph is used for decomposing the object, with the guiding principle that resulting sub-volumes are sweepable.  ...  The embedded Voronoi graph contains the full symbolic information of the Voronoi diagram and the medial axis of the object, and a geometric approximation to the real geometry.  ...  Part of this research was supported by the Israeli Ministry of Science, the program for development of scientific and technological infrastructures.  ... 
doi:10.1007/s003660050020 fatcat:2bwxoifa5zccvenhmok5t4huaa

Stable Sets in {ISK4,wheel}-Free Graphs

Martin Milanič, Irena Penev, Nicolas Trotignon
2017 Algorithmica  
A graph is {ISK4,wheel}-free if it has no ISK4 and does not contain a wheel as an induced subgraph.  ...  An ISK4 in a graph G is an induced subgraph of G that is isomorphic to a subdivision of K 4 (the complete graph on four vertices).  ...  Proof Let (G, w) be the input {ISK4,wheel}-free trigraph with n = |V (G)|. We first call the O(n 6 ) time algorithm from Theorem 4.8 with input G.  ... 
doi:10.1007/s00453-016-0255-3 fatcat:bqvzrmtngzdhpkfhjdcphoxvle

The (theta, wheel)-free graphs Part I: Only-prism and only-pyramid graphs

Emilie Diot, Marko Radovanović, Nicolas Trotignon, Kristina Vušković
2018 Journal of combinatorial theory. Series B (Print)  
In this paper, we prove two structure theorems: one for graphs with no thetas, wheels and prisms as induced subgraphs, and one for graphs with no thetas, wheels and pyramids as induced subgraphs.  ...  In Part II of this series we generalize these results to graphs with no thetas and wheels as induced subgraphs, and in Parts III and IV, using the obtained structure, we solve several optimization problems  ...  ] , graphs that do not contain K 4 or a wheel as a subgraph [33, 3] , propeller-free graphs [4] , graphs with no wheel or antiwheel [23] and planar wheel-free graphs [2] .  ... 
doi:10.1016/j.jctb.2017.12.004 fatcat:ddewr4xmb5gbnnluoomw7xmwly
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