Tight Lower Bounds on the Resolution Complexity of Perfect Matching Principles

2016 ◽  
Vol 145 (3) ◽  
pp. 229-242 ◽  
Author(s):  
Dmitry Itsykson ◽  
Vsevolod Oparin ◽  
Mikhail Slabodkin ◽  
Dmitry Sokolov
Keyword(s):  
Lower Bounds ◽  
Perfect Matching

scholarly journals Eigenvalues, traceability, and perfect matching of a graph

2021 ◽  
Vol 57 (3) ◽  
pp. 274-285
Author(s):  
V. I. Benediktovich
Keyword(s):  
Spectral Radius ◽  
Lower Bounds ◽  
Perfect Matching ◽  
Hamiltonian Path ◽  
Recognition Algorithm ◽  
Recognition Problem ◽  
Cyclomatic Number ◽  
Np Complete

It is well known that the recognition problem of the existence of a perfect matching in a graph, as well as the recognition problem of its Hamiltonicity and traceability, is NP-complete. Quite recently, lower bounds for the size and the spectral radius of a graph that guarantee the existence of a perfect matching in it have been obtained. We improve these bounds, firstly, by using the available bounds for the size of the graph for existence of a Hamiltonian path in it, and secondly, by finding new lower bounds for the spectral radius of the graph that are sufficient for the traceability property. Moreover, we develop the recognition algorithm of the existence of a perfect matching in a graph. This algorithm uses the concept of a (κ,τ)-regular set, which becomes polynomial in the class of graphs with a fixed cyclomatic number.

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds
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