Hamiltonicity and cycle extensions in 0-block-intersection graphs of balanced incomplete block designs

2015 ◽  
Vol 80 (3) ◽  
pp. 421-433 ◽  
Author(s):  
Jason T. LeGrow ◽  
David A. Pike ◽  
Jonathan Poulin
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Intersection Graphs ◽  
Balanced Incomplete Block Designs ◽  
Block Intersection ◽  
Balanced Incomplete Block

Classification of resolvable balanced incomplete block designs — the unitals on 28 points

2009 ◽  
Vol 59 (2) ◽  
Author(s):  
Petteri Kaski ◽  
Patric Östergård
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Doctoral Thesis ◽  
Parallel Class ◽  
Balanced Incomplete Block Designs ◽  
Balanced Incomplete Block

AbstractApproaches for classifying resolvable balanced incomplete block designs (RBIBDs) are surveyed. The main approaches can roughly be divided into two types: those building up a design parallel class by parallel class and those proceeding point by point. With an algorithm of the latter type — and by refining ideas dating back to 1917 and the doctoral thesis by Pieter Mulder — it is shown that the list of seven known resolutions of 2-(28, 4, 1) designs is complete; these objects are also known as the resolutions of unitals on 28 points.

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