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Hypergraph Isomorphism for Groups with Restricted Composition Factors

2020
*
International Colloquium on Automata, Languages and Programming
*

In particular, this gives an

doi:10.4230/lipics.icalp.2020.88
dblp:conf/icalp/Neuen20
fatcat:xa3qrjq3qzezrorjnkg7sdysqe
*isomorphism**test**for**graphs**of*Euler*genus*at most g running in time n^O((log g)^c). ... As an application*of*this result, we obtain,*for*example, an algorithm*testing**isomorphism**of**graphs*excluding K_{3,h} as a minor in time n^O((log h)^c). ... In particular, this gives an*isomorphism**test**for**graphs**of*Euler*genus*at most g running in time n O((log g) c ) . ...##
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A practical algorithm for the computation of the genus

2022
*
Ars Mathematica Contemporanea
*

We describe a practical algorithm to compute the (orientable)

doi:10.26493/1855-3974.2320.c2d
fatcat:ufr5bteqovgovdc2vapxky5jvy
*genus**of*a*graph*, give results*of*the program implementing this algorithm, and compare the performance to existing algorithms. ... The aim*of*this algorithm is to be fast enough*for*many applications instead*of*focusing on the theoretical asymptotic complexity. ...*For*these*tests*,*for*multi*genus*no lower*bound**for*the*genus*was computed. ...##
###
A Practical Algorithm for the Computation of the Genus
[article]

2020
*
arXiv
*
pre-print

We describe a practical algorithm to compute the (oriented)

arXiv:2005.08243v1
fatcat:eiibn3s44zctle4mp223tehbvq
*genus**of*a*graph*, give results*of*the program implementing this algorithm, and compare the performance to existing algorithms. ... The aim*of*this algorithm is to be fast enough*for*many applications instead*of*focusing on the theoretical asymptotic complexity. ...*For*these*tests*,*for*multi*genus*no lower*bound**for*the*genus*was computed. ...##
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The Graph Isomorphism Problem (Dagstuhl Seminar 15511)

2016
*
Dagstuhl Reports
*

A highlight

doi:10.4230/dagrep.5.12.1
dblp:journals/dagstuhl-reports/BabaiDST15
fatcat:meig4kvcgffnjiq5wpa6wjs6am
*of*the conference was the presentation*of*a new quasi-polynomial time algorithm*for*the*Graph**Isomorphism*Problem, providing the first improvement since 1983. ... This report documents the program and the outcomes*of*Dagstuhl Seminar 15511 "The*Graph**Isomorphism*Problem". ... Tinhofer noted that*isomorphism**testing**for*compact*graphs*can be done quite efficiently by linear programming. ...##
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Fixed-Point Definability and Polynomial Time
[chapter]

2009
*
Lecture Notes in Computer Science
*

A property P is definable in L if P = P φ

doi:10.1007/978-3-642-04027-6_4
fatcat:qajggupey5dq7gnn6mp2ehekny
*for*some sentence φ*of*L. ... Example Connectedness*of**graphs*, satisfiability*of*Boolean circuits, the language {a n b n | n ≥ 0} 6 Abstract Logics A logic L consists*of*a set*of*sentences and a semantics that associates a property ... Application to*Isomorphism**Testing*The k-dimensional Weisfeiler-Leman Algorithm (k-WL) is a simple combinatorial algorithm*for**testing**isomorphism**of**graphs*, based on an iterative "color refinement" on ...##
###
On the genera of polyhedral embeddings of cubic graph
[article]

2021
*
arXiv
*
pre-print

that number

arXiv:2008.09467v3
fatcat:lhjvaviqtbey3fh423rjykbi24
*of*vertices, and that there is no*bound*on the number*of*genera in which a cubic*graph*can have a polyhedral embedding. ... While these results suggest a large variety*of*polyhedral embeddings, computations*for*up to 28 vertices suggest that by far most*of*the cubic*graphs*do not have a polyhedral embedding in any*genus*and ... (a) What is (a good approximation*of*) the upper*bound*ζ 3 (2g)*for*the number*of*polyhedral embeddings*of*a cubic*graph*in a surface*of**genus*g? ...##
###
Graph Isomorphism Restricted by Lists
[article]

2016
*
arXiv
*
pre-print

:

arXiv:1607.03918v2
fatcat:rea4gbmazrbebbirsyhndky7mu
*for*trees, planar*graphs*, interval*graphs*, circle*graphs*, permutation*graphs*,*bounded**genus**graphs*, and*bounded*treewidth*graphs*. 3) Algorithms based on group theory do not translate: ListIso remains ... NP-complete*for*cubic colored*graphs*with sizes*of*color classes*bounded*by 8. ...*Bounded*Eigenvalue Multiplicity. The polynomial-time algorithms*for*GraphIso*of**graphs**of**bounded*eigenvalue multiplicity [6, 22] are heavily based on group theory. ...##
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Fixed-parameter tractability of graph isomorphism in graphs with an excluded minor

2022
*
Symposium on the Theory of Computing
*

We prove that

doi:10.1145/3519935.3520076
dblp:conf/stoc/LokshtanovPP022
fatcat:ablwm2hiyrdzlatyxi57ivtnje
*Graph**Isomorphism*and Canonization in*graphs*excluding a fixed*graph*𝐻 as a minor can be solved by an algorithm working in time 𝑓 (𝐻 ) • 𝑛 O (1) , where 𝑓 is some function. ...*bounded*treewidth. ... There, the goal is to obtain an isomorphisminvariant tree decomposition*of*the input*graph**of*width*bounded*in parameter; then, to*test**isomorphism**of*two*graphs*it suffices to*test**isomorphism**of*such ...##
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Surface Split Decompositions and Subgraph Isomorphism in Graphs on Surfaces
[article]

2011
*
arXiv
*
pre-print

The key to these improvements is the introduction

arXiv:1109.4554v1
fatcat:xnw762xzhbalnovrz77sb5bsye
*of*surface split decompositions*for**bounded**genus**graphs*, which generalize sphere cut decompositions*for*planar*graphs*. ... We generalize this result, by giving an algorithm*of*the same complexity*for**graphs*that can be embedded in surfaces*of**bounded**genus*. At the same time, we simplify the algorithm and analysis. ... Acknowledgement The author would like to thank Frederic Dorn*for*the introduction to the subject and the many inspiring discussions. ...##
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Surface Split Decompositions and Subgraph Isomorphism in Graphs on Surfaces

2012
*
Symposium on Theoretical Aspects of Computer Science
*

complexity

doi:10.4230/lipics.stacs.2012.531
dblp:conf/stacs/Bonsma12
fatcat:agte2kqezrbklpanbukiliyiiy
*for**graphs*that can be embedded in surfaces*of**bounded**genus*. ... The key to these improvements is the introduction*of*surface split decompositions*for**bounded**genus**graphs*, which generalize sphere cut decompositions*for*planar*graphs*. ... Acknowledgement The author would like to thank Frederic Dorn*for*the introduction to the subject and the many inspiring discussions. ...##
###
Recent Advances on the Graph Isomorphism Problem
[article]

2021
*
arXiv
*
pre-print

We give an overview

arXiv:2011.01366v2
fatcat:drrbl2cx3zabtkxo75f6nc5jlq
*of*recent advances on the*graph**isomorphism*problem. ... Our main focus will be on Babai's quasi-polynomial time*isomorphism**test*and subsequent developments that led to the design*of**isomorphism*algorithms with a quasi-polynomial parameterized running time ...*Graphs**of*Small*Genus*Next, we turn to the*isomorphism*problem*for**graphs**of**bounded*Euler*genus*. Recall that a*graph*has Euler*genus*at most g if it can be embedded on a surface*of*Euler*genus*g. ...##
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Isomorphism of k-contractible graphs. A generalization of bounded valence and bounded genus

1983
*
Information and Control
*

A polynomial time

doi:10.1016/s0019-9958(83)80047-3
fatcat:7hvtd2q4tnfn5drybtgqnxvvjm
*isomorphism**test**for**graphs*called k-contractible*graphs**for*fixed k is included. ... The class*of*k-contractible*graphs*includes the*graphs**of**bounded*valence and the*graphs**of**bounded**genus*. ...*Isomorphism**for*k-contractible*graphs*is polynomial time testable. THE*BOUNDED**GENUS*CASE Here we shall show that grai~hs*of**bounded**genus*are k-contractible*graphs*. ...##
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Computational complexity of reconstruction and isomorphism testing for designs and line graphs

2011
*
Journal of combinatorial theory. Series A
*

In this paper, we study the computational complexity

doi:10.1016/j.jcta.2010.06.006
fatcat:vxiuqw6zrjeqjab74skehfucnu
*of**isomorphism**testing**for*line*graphs**of*t-(v,k,λ) designs. ...*For*this class*of*highly regular*graphs*, we obtain a worst-case running time*of*O(v^ v + O(1))*for**bounded*parameters t,k,λ. ... Acknowledgments I thank Peter Hauck, Michael Kaufmann and Jacobo Torán*for*interesting discussions about*graph**isomorphism*, and*for*reading an early draft*of*this paper. ...##
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Page 3092 of Mathematical Reviews Vol. , Issue 94f
[page]

1994
*
Mathematical Reviews
*

In particular, a linear time algorithm

*for**testing**isomorphism**of**graphs**of**bounded*average*genus*is presented.” ... Summary: “Recent progress in topological*graph*theory has shown potential applicability*of*average*genus*to*graph**isomorphism**test*- ing. ...##
###
Tropically planar graphs
[article]

2020
*
arXiv
*
pre-print

We develop necessary conditions

arXiv:1908.04320v3
fatcat:lyqr2hk3snhcxddafayfcxhh2u
*for**graphs*to be tropically planar, and compute the number*of*tropically planar*graphs*up to*genus*7. ... We provide non-trivial upper and lower*bounds*on the number*of*tropically planar*graphs*, and prove that asymptotically 0%*of*connected trivalent planar*graphs*are tropically planar. ... In general, there is no known efficient way to*test*if a given*graph*is troplanar, although an algorithm*for*finding all troplanar*graphs**of*a fixed*genus*g was designed and implemented in [6] . ...
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