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Structure and Recognition of Graphs with No 6-wheel Subdivision

2008
*
Algorithmica
*

ÓÖ v 0 v 0 v 0

doi:10.1007/s00453-007-9162-y
fatcat:nbbbxru4nzb4rhpwgak2wdzcfy
*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 ...##
###
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

2018
*
Journal of Graph Theory
*

In this paper, we study the

doi:10.1002/jgt.22428
fatcat:3op75pg36zbo7a6572uys5v6ra
*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 ...##
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Search strategies for developing characterizations of graphs without small wheel subdivisions
[article]

2013
*
arXiv
*
pre-print

Proving a result for the

arXiv:1311.0574v1
fatcat:wn2ud2l6cnfpflzufhd3bkjolm
*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. ...##
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On graphs with no induced subdivision of K4

2012
*
Journal of combinatorial theory. Series B (Print)
*

We obtain also a

doi:10.1016/j.jctb.2012.04.005
fatcat:377entngsfd3xalcm5wq5hw3o4
*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. ...##
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On the reconstruction of planar graphs

2007
*
Journal of combinatorial theory. Series B (Print)
*

We show that the planarity

doi:10.1016/j.jctb.2006.12.005
fatcat:vzciptefoze6lfkdtfsonsytdq
*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] . ...##
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The existence of homeomorphic subgraphs in chordal graphs

1997
*
Applied Mathematics Letters
*

We establish conditions for the existence, in a chordal

doi:10.1016/s0893-9659(97)00027-x
fatcat:q4663fbr2vdzhkgsbj3u73gfoq
*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. ...##
###
Even-hole-free graphs: A survey

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*. ...

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

2020
*
arXiv
*
pre-print

In particular, we show that the 2-

arXiv:2003.08468v2
fatcat:diek3q7zd5hmtklr22zpkr6wqe
*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. ...##
###
Detecting induced subdivision of K_4
[article]

2017
*
arXiv
*
pre-print

In this paper, we propose a polynomial-time algorithm to test whether a given

arXiv:1703.04637v1
fatcat:e3e5vc5zybgjbp74carh7kwnim
*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*] . ...##
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Structure of classes of graphs defined by forbidding induced subgraphs
[article]

2013
*
arXiv
*
pre-print

This document is the Habilitation Thesis (Habilitation \'a Diriger des Recherches)

arXiv:1308.6678v1
fatcat:xgtoz7wi5nd7df3efa3lanoidq
*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. ...##
###
Detecting wheels

2014
*
Applicable Analysis and Discrete Mathematics
*

A

doi:10.2298/aadm131128023d
fatcat:ydgzkuf7ljbpxkocycqomvrezu
*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 ...##
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Hexahedral Mesh Generation using the Embedded Voronoi Graph

1999
*
Engineering with Computers
*

The embedded Voronoi

doi:10.1007/s003660050020
fatcat:2bwxoifa5zccvenhmok5t4huaa
*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. ...##
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Stable Sets in {ISK4,wheel}-Free Graphs

2017
*
Algorithmica
*

A

doi:10.1007/s00453-016-0255-3
fatcat:bqvzrmtngzdhpkfhjdcphoxvle
*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. ...##
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The (theta, wheel)-free graphs Part I: Only-prism and only-pyramid graphs

2018
*
Journal of combinatorial theory. Series B (Print)
*

In this paper, we prove two

doi:10.1016/j.jctb.2017.12.004
fatcat:ddewr4xmb5gbnnluoomw7xmwly
*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] . ...
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