Packing $A$-Paths in Group-Labelled Graphs via Linear Matroid Parity

2016 ◽  
Vol 30 (1) ◽  
pp. 474-492 ◽  
Author(s):  
Yutaro Yamaguchi
Keyword(s):  
Matroid Parity ◽  
Labelled Graphs

scholarly journals MET: a Java package for fast molecule equivalence testing

2020 ◽  
Vol 12 (1) ◽  
Author(s):  
Jördis-Ann Schüler ◽  
Steffen Rechner ◽  
Matthias Müller-Hannemann
Keyword(s):  
Chemical Properties ◽  
Graph Isomorphism ◽  
Isomorphism Problem ◽  
Equivalence Classes ◽  
Equivalence Testing ◽  
Equivalence Test ◽  
Graph Isomorphism Problem ◽  
2D Structure ◽  
Node Labels ◽  
Labelled Graphs

AbstractAn important task in cheminformatics is to test whether two molecules are equivalent with respect to their 2D structure. Mathematically, this amounts to solving the graph isomorphism problem for labelled graphs. In this paper, we present an approach which exploits chemical properties and the local neighbourhood of atoms to define highly distinctive node labels. These characteristic labels are the key for clever partitioning molecules into molecule equivalence classes and an effective equivalence test. Based on extensive computational experiments, we show that our algorithm is significantly faster than existing implementations within , and . We provide our Java implementation as an easy-to-use, open-source package (via GitHub) which is compatible with . It fully supports the distinction of different isotopes and molecules with radicals.

Parallel algorithms for matroid intersection and matroid parity

2015 ◽  
Vol 07 (02) ◽  
pp. 1550019
Author(s):  
Jinyu Huang
Keyword(s):  
Parallel Algorithms ◽  
Polynomial Identity ◽  
Black Box ◽  
Matroid Intersection ◽  
Polynomial Identity Testing ◽  
Identity Testing ◽  
Common Base ◽  
Graphic Matroid ◽  
Matroid Parity ◽  
Nc Algorithms

A maximum linear matroid parity set is called a basic matroid parity set, if its size is the rank of the matroid. We show that determining the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity) is in NC2, provided that there are polynomial number of common bases (basic matroid parity sets). For graphic matroids, we show that finding a common base for matroid intersection is in NC2, if the number of common bases is polynomial bounded. To our knowledge, these algorithms are the first deterministic NC algorithms for matroid intersection and matroid parity. We also give a new RNC2 algorithm that finds a common base for graphic matroid intersection. We prove that if there is a black-box NC algorithm for Polynomial Identity Testing (PIT), then there is an NC algorithm to determine the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity).

An augmenting path algorithm for linear matroid parity

COMBINATORICA ◽  
1986 ◽  
Vol 6 (2) ◽  
pp. 123-150 ◽  
Author(s):  
Harold N. Gabow ◽  
Matthias Stallmann
Keyword(s):  
Augmenting Path ◽  
Matroid Parity

Combinatorial entanglement: detecting entanglement in quantum states using grid-labelled graphs

2017 ◽  
Vol 61 ◽  
pp. 819-825 ◽  
Author(s):  
Joshua Lockhart ◽  
Otfried Gühne ◽  
Simone Severini
Keyword(s):  
Quantum States ◽  
Labelled Graphs

A Variational Model on Labelled Graphs with Cusps and Crossings

2015 ◽  
pp. 1-24 ◽  
Author(s):  
Giovanni Bellettini ◽  
Valentina Beorchia ◽  
Maurizio Paolini ◽  
Franco Pasquarelli
Keyword(s):  
Variational Model ◽  
Labelled Graphs

scholarly journals On matroid parity and matching polytopes

2020 ◽  
Vol 284 ◽  
pp. 322-331
Author(s):  
Konstantinos Kaparis ◽  
Adam N. Letchford ◽  
Ioannis Mourtos
Keyword(s):  
Matching Polytopes ◽  
Matroid Parity

Random Graphs from a Minor-Closed Class

2009 ◽  
Vol 18 (4) ◽  
pp. 583-599 ◽  
Author(s):  
COLIN McDIARMID
Keyword(s):  
Poisson Distribution ◽  
Random Graph ◽  
Generating Function ◽  
Random Graphs ◽  
Giant Component ◽  
Closed Class ◽  
Exponential Generating Function ◽  
Excluded Minor ◽  
A Minor ◽  
Labelled Graphs

A minor-closed class of graphs is addable if each excluded minor is 2-connected. We see that such a classof labelled graphs has smooth growth; and, for the random graphRnsampled uniformly from then-vertex graphs in, the fragment not in the giant component asymptotically has a simple ‘Boltzmann Poisson distribution’. In particular, asn→ ∞ the probability thatRnis connected tends to 1/A(ρ), whereA(x) is the exponential generating function forand ρ is its radius of convergence.

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