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pro vyhledávání: '"Lavollée, Jérémy"'
Autor:
Lavollée, Jérémy, Swanepoel, Konrad
A matchstick graph is a plane graph with edges drawn as unit-distance line segments. Harborth introduced these graphs in 1981 and conjectured that the maximum number of edges for a matchstick graph on $n$ vertices is $\lfloor 3n-\sqrt{12n-3} \rfloor$
Externí odkaz:
http://arxiv.org/abs/2209.09800
Autor:
Lavollée, Jérémy, Swanepoel, Konrad J.
A matchstick graph is a crossing-free unit-distance graph in the plane. Harborth (1981) proposed the problem of determining whether there exists a matchstick graph in which every vertex has degree exactly $5$. In 1982, Blokhuis gave a proof of non-ex
Externí odkaz:
http://arxiv.org/abs/2206.03956
Autor:
Lavollée, Jérémy, Swanepoel, Konrad J.
We show that a matchstick graph with $n$ vertices has no more than $3n-c\sqrt{n-1/4}$ edges, where $c=\frac12(\sqrt{12} + \sqrt{2\pi\sqrt{3}})$. The main tools in the proof are the Euler formula, the isoperimetric inequality, and an upper bound for t
Externí odkaz:
http://arxiv.org/abs/2108.07522
Autor:
Lavollée, Jérémy, Swanepoel, Konrad
Publikováno v:
Discrete & Computational Geometry; Dec2024, Vol. 72 Issue 4, p1530-1544, 15p
Akademický článek
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Autor:
Lavollée, Jérémy, Swanepoel, Konrad
Publikováno v:
SIAM Journal on Discrete Mathematics. 36:777-785
We show that a matchstick graph with $n$ vertices has no more than $3n-c\sqrt{n-1/4}$ edges, where $c=\frac12(\sqrt{12} + \sqrt{2\pi\sqrt{3}})$. The main tools in the proof are the Euler formula, the isoperimetric inequality, and an upper bound for t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0daeb6f66b7bee2625cc6ad832929d5b
https://doi.org/10.1137/21m1441134
https://doi.org/10.1137/21m1441134