Publication: The full metamorphosis of λ-fold designs into λ-fold 3-star systems
Program
KU-Authors
KU Authors
Co-Authors
N/A
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Publication Date
Language
English
Type
Journal Title
Journal ISSN
Volume Title
Abstract
Let (X, B) be a λ-fold λ-design. If a triangle is removed from each block of B the resulting collection of 3-stars; 5, is a partial λ-fold 3-star system; (X, S). If the edges belonging to the deleted triangles can be arranged into a collection of 3-stars T} then (X,S UT) is a A-fold 3-star system, called a metamorphosis of the A-fold K-design (X, B) into a A-fold 3-star system. Label the elements of each block 6 with b1,b2,b3 and 64 (in any manner). For each i = 1,2,3,4 define a set of triangles Ti and a set of stars S as follows: For each block b= [b1,b2,b3,b4) belonging to B) partition 6 into a star centered at 6 and the triangle b\ b, then place the star in Si and the triangle in T. (X, Si) forms a partial A-fold 3-star system. Now if the edges belonging to the triangles in T< can be arranged into a collection of stars Tthen (X, Si U T/) is a A-fold 3-star system and we say that Mi =(X, Si U T) is the ith metamorphosis of (X, B).
Description
Source:
Utilitas Mathematica
Publisher:
Utilitas Mathematica Publishing Inc.
Keywords:
Subject
Cycle decomposition, Graph, Steiner triple system