Edge list multicoloring trees: An extension of Hall's theorem

2003 ◽  
Vol 42 (3) ◽  
pp. 246-255 ◽  
Author(s):  
Mathew Cropper ◽  
András Gyárfás ◽  
Jenő Lehel
Keyword(s):  
Hall's Theorem ◽  
Edge List ◽  
Hall’S Theorem

A generalization of Hall’s theorem

2016 ◽  
Vol 10 (02) ◽  
pp. 1750024
Author(s):  
Feng Zhou
Keyword(s):  
Finite Group ◽  
Prime Divisors ◽  
Hall's Theorem ◽  
A Finite Group ◽  
Hall’S Theorem

Let [Formula: see text] be a finite group, whose order has [Formula: see text] prime divisors. In this paper, we prove that if [Formula: see text] has a [Formula: see text]-complement for [Formula: see text] prime divisors [Formula: see text] of [Formula: see text] and [Formula: see text] has no section isomorphic to [Formula: see text]. Then [Formula: see text] is solvable, which generalizes a theorem of Hall.

scholarly journals Hall's theorem and extending partial latinized rectangles

2015 ◽  
Vol 130 ◽  
pp. 26-41
Author(s):  
J.L. Goldwasser ◽  
A.J.W. Hilton ◽  
D.G. Hoffman ◽  
Sibel Özkan
Keyword(s):  
Hall's Theorem ◽  
Hall’S Theorem

A Generalization of Hall's Theorem: 10701

2001 ◽  
Vol 108 (10) ◽  
pp. 982 ◽  
Author(s):  
Fred Galvin
Keyword(s):  
Hall's Theorem ◽  
Hall’S Theorem

Factoring Graphs

2017 ◽  
Author(s):  
Arthur Benjamin ◽  
Gary Chartrand ◽  
Ping Zhang
Keyword(s):  
Graph Theory ◽  
Bipartite Graphs ◽  
Petersen Graph ◽  
Different Types ◽  
Bridgeless Graph ◽  
Hall's Theorem ◽  
Hall’S Theorem

This chapter focuses on Hall's Theorem, introduced by British mathematician Philip Hall, and its connection to graph theory. It first considers problems that ask whether some collection of objects can be matched in some way to another collection of objects, with particular emphasis on how different types of schedulings are possible using a graph. It then examines one popular version of Hall's work, a statement known as the Marriage Theorem, the occurrence of matchings in bipartite graphs, Tutte's Theorem, Petersen's Theorem, and the Petersen graph. Peter Christian Julius Petersen introduced the Petersen graph to show that a cubic bridgeless graph need not be 1-factorable. The chapter concludes with an analysis of 1-factorable graphs, the 1-Factorization Conjecture, and 2-factorable graphs.

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