New results on path-decompositions and their down-links
Anna Benini, Luca Giuzzi, Anita Pasotti
TL;DR
This paper investigates spectrum problems for path-decompositions in graph designs, focusing on down-links from (K_v, G)-designs to (K_n, P4)-designs, and presents general existence results for such decompositions.
Contribution
It introduces new spectrum results for path-decompositions and embeddings, advancing the understanding of down-links in graph design theory.
Findings
Spectrum problems for G' = P4 are solved.
General existence results for path-decompositions are provided.
Foundations for constructing down-links in graph designs are established.
Abstract
In (arXiv:1004.4127) the concept of down-link from a (K_v, G)-design B to a (K_n, G')-design B' has been introduced. In the present paper the spectrum problems for G'= P4 are studied. General results on the existence of path-decompositions and embeddings between path- decompositions playing a fundamental role for the construction of down-links are also presented
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Taxonomy
Topicsgraph theory and CDMA systems · Finite Group Theory Research · Coding theory and cryptography