arXiv subjects

Mario Gionfriddo

Publications and source records attributed to Mario Gionfriddo.

5 recordsLinked to original sources

arXiv2025

A construction of Steiner Triple Systems of type $v\longrightarrow 2v+7$

A Steiner Triple System ($STS$) of order $v$ is a hypergraph uniform of rank 3, with $v$ vertices and such that every 2-subset of vertices has degree 1. In this paper we give a construction, by difference method, of type $v\longrightarrow 2v+7$ with $v=2^n-7$, which means that, given an $STS$ of order $v=2^n -7$, it is always possible to construct an $STS$ of order $2^{n+1}-7$. Through this construction it is possible to get for any $n\ge 5$ an $STS(2^n-7)$ with a maximal independent set of maximal cardinality and which is $(n-1)$-bicolorable.

math.CO↗

arXiv2021

A short proof of the conjecture of Erdös--Straus for every $n\equiv 13 \textrm{ mod }24$

The Erdös--Straus conjecture states that the equation $\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ has positive integer solutions $x,y,z$ for every postive integers $n\geq 2$. In this short note we find explicity the solutions of the famous conjecture for the case $n\equiv13 \textrm{ mod } 24.$

math.NT↗

arXiv2020

Complex uniformly resolvable decompositions of $K_v$

In this paper we consider the complex uniformly resolvable decompositions of the complete graph $K_v$ into subgraphs such that each resolution class contains only blocks isomorphic to the same graph from a given set $\mathcal H$. We completely determine the spectrum for the cases $\mathcal{H} = \{K_2, P_3, K_3\}$, $\mathcal{H} = \{P_4, C_4\}$, and $\mathcal{H} = \{K_2, P_4, C_4\}$.

math.CO↗

arXiv2015

Resolvable h-sun designs

In this article we completely determine the spectrum for uniformly resolvable decompositions of the complete graph K_v into r 1-factors and s classes containing only copies of h-suns.

math.CO↗

arXiv2015

Resolvable G-designs of order v and index λ

In this paper we consider the problem concerning the existence of a resolvable G-design of order v and index λ. We solve the problem for the cases in which G is a connected subgraph of K_4.

math.CO↗