Zobrazeno 1 - 10
of 69
pro vyhledávání: '"Maffucci, Riccardo W."'
Autor:
De March, Ruben, Maffucci, Riccardo W.
We investigate several properties of Kronecker (direct, tensor) products of graphs that are planar and $3$-connected (polyhedral, $3$-polytopal). This class of graphs was recently characterised and constructed by the second author [15]. Our main resu
Externí odkaz:
http://arxiv.org/abs/2411.13473
We classify and construct all line graphs that are $3$-polytopes (planar and $3$-connected). Apart from a few special cases, they are all obtained starting from the medial graphs of cubic (i.e., $3$-regular) $3$-polytopes, by applying two types of gr
Externí odkaz:
http://arxiv.org/abs/2404.07819
Autor:
Maffucci, Riccardo W.
We give a complete classification of the Kronecker (i.e. direct) product graphs that are planar and $3$-connected (i.e. $3$-polytopal). They are all of the form \[H\wedge K_2,\] where $H$ is a $2$-connected graph, possibly non-planar, and satisfying
Externí odkaz:
http://arxiv.org/abs/2402.01407
The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers [RW08, ORW08]. In this paper we study the correlation structure among different functionals such as nodal length, bo
Externí odkaz:
http://arxiv.org/abs/2312.13166
Autor:
Maffucci, Riccardo W.
Recent literature posed the problem of characterising the graph degree sequences with exactly one $3$-polytopal (i.e. planar, $3$-connected) realisation. This seems to be a difficult problem in full generality. In this paper, we characterise the sequ
Externí odkaz:
http://arxiv.org/abs/2308.12853
Autor:
Maffucci, Riccardo W.
Publikováno v:
European Journal of Combinatorics (2024+)
A $3$-polytope is a $3$-connected, planar graph. It is called unigraphic if it does not share its vertex degree sequence with any other $3$-polytope, up to graph isomorphism. The classification of unigraphic $3$-polytopes appears to be a difficult pr
Externí odkaz:
http://arxiv.org/abs/2305.20012
Autor:
Maffucci, Riccardo W.
We consider the graph degree sequences such that every realisation is a polyhedron. It turns out that there are exactly eight of them. All of these are unigraphic, in the sense that each is realised by exactly one polyhedron. This is a revisitation o
Externí odkaz:
http://arxiv.org/abs/2305.15063
Autor:
Delitroz, Jim, Maffucci, Riccardo W.
A sequence $\sigma$ of $p$ non-negative integers is unigraphic if it is the degree sequence of exactly one graph, up to isomorphism. A polyhedral graph is a $3$-connected, planar graph. We investigate which sequences are unigraphic with respect to th
Externí odkaz:
http://arxiv.org/abs/2301.08021
A polyhedral graph is a $3$-connected planar graph. We find the least possible order $p(k,a)$ of a polyhedral graph containing a $k$-independent set of size $a$ for all positive integers $k$ and $a$. In the case $k = 1$ and $a$ even, we prove that th
Externí odkaz:
http://arxiv.org/abs/2212.14323
Autor:
Maffucci, Riccardo W., Willems, Niels
The $3$-polytopes are planar, $3$-connected graphs. A classical question is, for $r\geq 3$, is the $2(r-1)$-gonal prism $K_2\times C_{2(r-1)}$ the unique $3$-polytope of graph radius $r$ and smallest size? Under some extra assumptions, we answer this
Externí odkaz:
http://arxiv.org/abs/2207.04743