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Lovász Meets Weisfeiler and Leman [article]

Holger Dell, Martin Grohe, Gaurav Rattan
2018 arXiv   pre-print
known as the 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.  ... 
arXiv:1802.08876v2 fatcat:clduredu25azpfhzroddazj6ha

Lovász Meets Weisfeiler and Leman

Holger Dell, Martin Grohe, Gaurav Rattan
2018
as the 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).  ... 
doi:10.18154/rwth-2018-231956 fatcat:lwbwe7s6tfenrlosorutlwwcly

Algorithmic Data Science (Invited Talk)

Petra Mutzel, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
ACM Subject Classification Theory of computation → Design 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.  ... 
doi:10.4230/lipics.stacs.2019.3 dblp:conf/stacs/Mutzel19 fatcat:4sq6azx2snb2tkhr4n5wchaoyq

Graph isomorphism: Physical resources, optimization models, and algebraic characterizations [article]

Laura Mančinska, David E. Roberson, Antonios Varvitsiotis
2020 arXiv   pre-print
Our techniques are an interesting mix of algebra, combinatorics, optimization, 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  ... 
arXiv:2004.10893v1 fatcat:wnophwxi5jbhbcf4msnn56co3u

Quantum isomorphism is equivalent to equality of homomorphism counts from planar graphs [article]

Laura Mančinska, David E. Roberson
2019 arXiv   pre-print
Over 50 years ago, 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  ... 
arXiv:1910.06958v2 fatcat:i2ckcwtqbvhzvhbab6hxuw3vy4

Mini-Workshop: Exploiting Symmetry in Optimization

Volker Kaibel, Leo Liberti, Achill Schürmann, Renata Sotirov
2010 Oberwolfach Reports  
Given a (vertex 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.  ... 
doi:10.4171/owr/2010/38 fatcat:n2zcqzooonex7d3kcknkfsxpxa

RaWaNet: Enriching Graph Neural Network Input via Random Walks on Graphs [article]

Anahita Iravanizad, Edgar Ivan Sanchez Medina, Martin Stoll
2021 arXiv   pre-print
Namely, (regular) walks of length 1 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.  ... 
arXiv:2109.07555v3 fatcat:xnx5yerrcnbe5kuxw5gzbzf6sq

Graph Isomorphism in Quasipolynomial Time [article]

László Babai
2016 arXiv   pre-print
The affected/unaffected dichotomy underlies the core "local certificates" routine 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).  ... 
arXiv:1512.03547v2 fatcat:nfilvn466zhafloxxlyeqitmre

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

E Konstantinova, D Krotov, A Mednykh, Rina Khomyakova, Elena Konstantinova, Denis Krotov, Alexey Medvedev, E Konstantinova, D Krotov, A Mednykh
2016 unpublished
The International Conference 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  ... 
fatcat:do352qvjsbg7jf6ykjdccc6rfy

Between primitive and 2-transitive: Synchronization and its friends

João Araújo, Peter Cameron, Benjamin Steinberg
2017 EMS Surveys in Mathematical Sciences  
Coherent configurations were introduced independently by Donald Higman [53, 54] in the USA 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.  ... 
doi:10.4171/emss/4-2-1 fatcat:p4wgh52hhnghdcjau3wmokss2m

Minimal matrices in the Bruhat order for symmetric (0,1)-matrices

Henrique F. da Cruz, Rosário Fernandes, Susana Furtado
2017 Linear Algebra and its Applications  
graph theory 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.  ... 
doi:10.1016/j.laa.2017.05.014 fatcat:zlcp5rb2sjeqvlyaajvf2nyoby