Minimum embedding of STSs into<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si54.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>e</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-systems

Gionfriddo, Mario; Quattrocchi, Gaetano; Ragusa, Giorgio

doi:10.1016/j.disc.2013.03.015

Cited by 2 publications

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The embedding problems have interesting applications to networks ( [5]), that is why they have been investigated in several papers. In particular, the minimum embedding problem of STSs into G-designs have been studied in the case when G = K 4 , G = K 4 −e (the complete graph on four vertices with one deleted edge), or G = K 3 + e (a kite, i.e., a triangle with one pendant edge) have been solved in [3], [4], [9], [14].…”

Section: Introductionmentioning

confidence: 99%

Minimum embedding of any Steiner triple system into a 3-sun system via matchings

Faro¹,

Tripodi²

2020

Preprint

View full text Add to dashboard Cite

Let G be a simple finite graph and G ′ be a subgraph of G. A G ′ -design (X, B) of order n is said to be embedded into a G-design (X ∪ U, C) of order n + u, if there is an injective function f : B → C such that B is a subgraph of f (B) for every B ∈ B. The function f is called an embedding of (X, B) into (X ∪ U, C). If u attains the minimum possible value, then f is a minimum embedding. Here, by means of König's Line Coloring Theorem and edge coloring properties a complete solution is given to the problem of determining a minimum embedding of any K 3 -design (well-known as Steiner Triple System or, shortly, STS) into a 3-sun system or, shortly, a 3SS (i.e., a G-design where G is a graph on six vertices consisting of a triangle with three pendant edges which form a 1-factor).

show abstract