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Lovász Meets Weisfeiler and Leman
[article]

2018
*
arXiv
*
pre-print

known as the

arXiv:1802.08876v2
fatcat:clduredu25azpfhzroddazj6ha
*Weisfeiler*-*Leman*algorithm. ... We lift the results for trees to an equivalence between numbers of homomorphisms from graphs of tree width k, the k-dimensional*Weisfeiler*-*Leman*algorithm,*and*the level-k Sherali-Adams relaxation of our ... XX:4*Lovász**Meets**Weisfeiler**and**Leman*Figure 1 Two fractionally non-isomorphic graphs with the same path homomorphism counts. Theorem 2. ...##
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Lovász Meets Weisfeiler and Leman

2018

as the

doi:10.18154/rwth-2018-231956
fatcat:lwbwe7s6tfenrlosorutlwwcly
*Weisfeiler*-*Leman*algorithm. ... We lift the results for trees to an equivalence between numbers of homomorphisms from graphs of tree width k, the k-dimensional*Weisfeiler*-*Leman*algorithm,*and*the level-k Sherali-Adams relaxation of our ... Since*Lovász**Meets**Weisfeiler**and**Leman*Now suppose HOM r (G) = HOM r (H) holds,*and*set v = HOM r (G). ...##
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Algorithmic Data Science (Invited Talk)

2019
*
Symposium on Theoretical Aspects of Computer Science
*

ACM Subject Classification Theory of computation → Design

doi:10.4230/lipics.stacs.2019.3
dblp:conf/stacs/Mutzel19
fatcat:4sq6azx2snb2tkhr4n5wchaoyq
*and*analysis of algorithms; Theory of computation → Graph algorithms analysis; Theory of computation → Complexity theory*and*logic; Mathematics ... ., [48]*and*[42] . ... data cleaning, data analysis*and*visualisation. ...##
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Graph isomorphism: Physical resources, optimization models, and algebraic characterizations
[article]

2020
*
arXiv
*
pre-print

Our techniques are an interesting mix of algebra, combinatorics, optimization,

arXiv:2004.10893v1
fatcat:wnophwxi5jbhbcf4msnn56co3u
*and*quantum information. ... a verifier interacts with two non-communicating players (called provers) by privately sending each of them a random vertex from either G or H, whose aim is to convince the verifier that two graphs G*and*... As it turns out, the notion of DN N -isomorphism coincides with an equivalence relation on graphs introduced in 1968 by*Weisfeiler**and**Leman*[29] , known today as the 2-dimensional*Weisfeiler*-*Leman*method ...##
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Quantum isomorphism is equivalent to equality of homomorphism counts from planar graphs
[article]

2019
*
arXiv
*
pre-print

Over 50 years ago,

arXiv:1910.06958v2
fatcat:i2ckcwtqbvhzvhbab6hxuw3vy4
*Lovász*proved that two graphs are isomorphic if*and*only if they admit the same number of homomorphisms from any graph [Acta Math. Hungar. 18 (1967), pp. 321–328]. ... In this work we prove that two graphs are quantum isomorphic (in the commuting operator framework) if*and*only if they admit the same number of homomorphisms from any planar graph. ... DR: I would like to acknowledge the helpful discussions with Arthur Chassaniol concerning intertwiners of quantum automorphism groups which took place at the 'Cohomology of quantum groups*and*quantum automorphism ...##
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Mini-Workshop: Exploiting Symmetry in Optimization

2010
*
Oberwolfach Reports
*

Given a (vertex

doi:10.4171/owr/2010/38
fatcat:n2zcqzooonex7d3kcknkfsxpxa
*and*edge) weighted graph Γ with adjacency matrix A(Γ), there is unique minimal (w.r.t. d) CC s.t. A(Γ) = A∈A c A A, computable by*Weisfeiler*-*Leman*stabilization in polynomial time. ... If Schur were right we would have had a polynomial-time algorithm for graph isomorphism (*Weisfeiler*-*Leman*stabilization would be recognizing isomorphic graphs). ... Generating sets*and*generating functions under symmetry Matthias Köppe Generating sets. Let C ⊂ R n be a pointed rational polyhedral cone. ...##
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RaWaNet: Enriching Graph Neural Network Input via Random Walks on Graphs
[article]

2021
*
arXiv
*
pre-print

Namely, (regular) walks of length 1

arXiv:2109.07555v3
fatcat:xnx5yerrcnbe5kuxw5gzbzf6sq
*and*2,*and*a fractional walk of length γ∈ (0,1), in order to capture the different local*and*global dynamics on the graphs. ... The majority of GNN architectures are designed based on developing new convolutional*and*/or pooling layers that better extract the hidden*and*deeper representations of the graphs to be used for different ... They defined a local*and*global neighborhood for their introduced higher dimensional graph, which is based on higher order*Weisfeiler*-*Leman*graph isomorphisms. ...##
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Graph Isomorphism in Quasipolynomial Time
[article]

2016
*
arXiv
*
pre-print

The affected/unaffected dichotomy underlies the core "local certificates" routine

arXiv:1512.03547v2
fatcat:nfilvn466zhafloxxlyeqitmre
*and*is the central divide-*and*-conquer tool of the algorithm. ... We show that the Graph Isomorphism (GI) problem*and*the related problems of String Isomorphism (under group action) (SI)*and*Coset Intersection (CI) can be solved in quasipolynomial ((( n)^O(1))) time. ... So T Jh (x, y) is the maximum of T (G, ϕ) over all G*and*ϕ with the parameters n ≤ x*and*m ≤ y. Moreover, T Jh (x) is defined as T Jh (x) = T Jh (x, x). ...##
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СИБИРСКИЕ ЭЛЕКТРОННЫЕ МАТЕМАТИЧЕСКИЕ ИЗВЕСТИЯ Special issue: Graphs and Groups, Spectra and Symmetries-G2S2 2016 ON GRAPHS AND GROUPS, SPECTRA AND SYMMETRIES HELD ON AUGUST 15-28, 2016, NOVOSIBIRSK, RUSSIA

2016
unpublished

The International Conference

fatcat:do352qvjsbg7jf6ykjdccc6rfy
*and*PhD-Master Summer School on Graphs*and*Groups, Spectra*and*Symmetries (G2S2) were held on August 15-28, 2016, in Novosibirsk, Akademgorodok, Russia. ... The main goal of these events was to bring together young researchers*and*famous mathematicians in the field of graph theory*and*group theory, especially those involving group actions on combinatorial ... The importance of this notion was explained by the fact that if the coherent configuration of a graph is separable, then the isomorphism of this graph to any other graph can be tested by the*Weisfeiler*-*Leman*...##
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Between primitive and 2-transitive: Synchronization and its friends

2017
*
EMS Surveys in Mathematical Sciences
*

Coherent configurations were introduced independently by Donald Higman [53, 54] in the USA

doi:10.4171/emss/4-2-1
fatcat:p4wgh52hhnghdcjau3wmokss2m
*and*by*Weisfeiler**and**Leman*[102] in the former Soviet Union to describe the orbits on pairs of a permutation ... Now 3-sets in the same S(L)*meet*in 0 or 2 points. So any image of the Fano plane*meets*each S(L) in at most (*and*hence exactly) one set. ...##
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Minimal matrices in the Bruhat order for symmetric (0,1)-matrices

2017
*
Linear Algebra and its Applications
*

graph theory

doi:10.1016/j.laa.2017.05.014
fatcat:zlcp5rb2sjeqvlyaajvf2nyoby
*and*combinatorics. ... We have received 150 abstracts for 20-minute contributed talks which will run in four parallel sessions*and*cover a large variety of areas within graph theory*and*combinatorics. ... The boundary-type sets are rather trivial for trees*and*are all subsets of the leaves. We provide a characterization of ∂(G), Ct(G),*and*Ext(G) for the family of MOPs. ...