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Detecting and Counting Small Subgraphs, and Evaluating a Parameterized Tutte Polynomial: Lower Bounds via Toroidal Grids and Cayley Graph Expanders [article]

Marc Roth, Johannes Schmitt, Philip Wellnitz
2021 arXiv   pre-print
As a main technical result, we gain a complete understanding of the coefficients of toroidal grids and selected Cayley graph expanders in the homomorphism basis of #𝙴𝚍𝚐𝚎𝚂𝚞𝚋(Φ).  ...  Our methods can also be applied to a parameterized variant of the Tutte Polynomial T^k_G of a graph G, to which many known combinatorial interpretations of values of the (classical) Tutte Polynomial can  ...  Acknowledgements We thank Alina Vdovina and Norbert Peyerimhoff for explaining their construction of 2-group Cayley graph expanders [65] .  ... 
arXiv:2011.03433v2 fatcat:7aauf7xejvfx5atw3n7s6sefsa

Detecting and Counting Small Subgraphs, and Evaluating a Parameterized Tutte Polynomial: Lower Bounds via Toroidal Grids and Cayley Graph Expanders

Marc Roth, Johannes Schmitt, Philip Wellnitz, Nikhil Bansal, Emanuela Merelli, James Worrell
2021
As a main technical result, we gain a complete understanding of the coefficients of toroidal grids and selected Cayley graph expanders in the homomorphism basis of #EdgeSub(Φ).  ...  As a special case of such a linear combination, we introduce a parameterized variant of the Tutte Polynomial T^k_G of a graph G, to which many known combinatorial interpretations of values of the (classical  ...  = 0 mod ℓ . (2) Detecting and Counting Small Subgraphs, and a Parameterized Tutte Polynomial #EdgeSub(Φ) and EdgeSub(Φ).  ... 
doi:10.4230/lipics.icalp.2021.108 fatcat:7x7aye2agrbh3ivumgwrw5j2km

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
Finally I report numerical results of a comparison between the variant and a minimization approach using penalty functions.  ...  It is shown that for the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral  ...  Heuristics and lower bounds are evaluated on randomly generated test problems.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa

A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas Compiled by

Thomas Zaslavsky
1996 unpublished
Also, trees that yield identical two-graphs are characterized. (TG) 2007a Orbit counting and the Tutte polynomial.  ...  Examples: Planar, cylindrical, and toroidal grids with product signatures; line graphs of those grids and of +K n and −K n . [Annot. 19 Oct 2010.] (SG: Bal, Adj, LG) Anna Maria Ghirlanda See L.  ...  Main Theorem: For a simple, connected signed graph of order n and size |E| = m, the frustration index l (1981a) has a lower bound on D.]  ... 
fatcat:os5lveptfbbbplmcy4drb2zd3m