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pro vyhledávání: '"Zerafa, Jean Paul"'
Let $G$ be a bridgeless cubic graph. In 2023, the three authors solved a conjecture (also known as the $S_4$-Conjecture) made by Mazzuoccolo in 2013: there exist two perfect matchings of $G$ such that the complement of their union is a bipartite subg
Externí odkaz:
http://arxiv.org/abs/2309.06944
Let $G$ be a graph of even order, and consider $K_G$ as the complete graph on the same vertex set as $G$. A perfect matching of $K_G$ is called a pairing of $G$. If for every pairing $M$ of $G$ it is possible to find a perfect matching $N$ of $G$ suc
Externí odkaz:
http://arxiv.org/abs/2307.04545
Publikováno v:
J. Combin. Theory Ser. B 160, 1--14 (2023). Share Link: https://authors.elsevier.com/a/1gKfKLpTmV29P
Let $G$ be a bridgeless cubic graph. The Berge--Fulkerson Conjecture (1970s) states that $G$ admits a list of six perfect matchings such that each edge of $G$ belongs to exactly two of these perfect matchings. If answered in the affirmative, two othe
Externí odkaz:
http://arxiv.org/abs/2204.10021
Autor:
Gauci, John Baptist, Zerafa, Jean Paul
In 2015, Bogdanowicz gave a necessary and sufficient condition for a 4-regular circulant graph to be isomorphic to the Cartesian product of two cycles. Accordion graphs, denoted by $A[n,k]$, are 4-regular graphs on two parameters $n$ and $k$ which we
Externí odkaz:
http://arxiv.org/abs/2111.05725
Publikováno v:
Discrete Appl. Math. 337, 246--256 (2023). Share Link: https://authors.elsevier.com/c/1h8WP,3nuHsmJ6
Let $H$ and $G$ be graphs. An $H$-colouring of $G$ is a proper edge-colouring $f:E(G)\rightarrow E(H)$ such that for any vertex $u\in V(G)$ there exists a vertex $v\in V(H)$ with $f\left (\partial_Gu\right )=\partial_Hv$, where $\partial_Gu$ and $\pa
Externí odkaz:
http://arxiv.org/abs/2110.13684
Publikováno v:
Electron. J. Comb. 30, No. 2, Research Paper P2.5, 20 pgs. (2023)
A Hamiltonian graph is 2-factor Hamiltonian (2FH) if each of its 2-factors is a Hamiltonian cycle. A similar, but weaker, property is the Perfect-Matching-Hamiltonian property (PMH-property): a graph admitting a perfect matching is said to have this
Externí odkaz:
http://arxiv.org/abs/2109.03060
Autor:
Abreu, Marién, Gauci, John Baptist, Labbate, Domenico, Romaniello, Federico, Zerafa, Jean Paul
Publikováno v:
Ars Math. Contemp. 23, No. 3, #P3.01 (2023)
A graph $G$ has the Perfect-Matching-Hamiltonian property (PMH-property) if for each one of its perfect matchings, there is another perfect matching of $G$ such that the union of the two perfect matchings yields a Hamiltonian cycle of $G$. The study
Externí odkaz:
http://arxiv.org/abs/2106.00513
Publikováno v:
In European Journal of Combinatorics March 2024 117
The rook graph is a graph whose edges represent all the possible legal moves of the rook chess piece on a chessboard. The problem we consider is the following. Given any set $M$ containing pairs of cells such that each cell of the $m_1 \times m_2$ ch
Externí odkaz:
http://arxiv.org/abs/2104.01578
Autor:
Gauci, John Baptist, Zerafa, Jean Paul
Publikováno v:
Note Mat. 41, No. 2, 1-8 (2021)
The Erd\H{o}s--Faber--Lov\'{a}sz Conjecture, posed in 1972, states that if a graph $G$ is the union of $n$ cliques of order $n$ (referred to as defining $n$-cliques) such that two cliques can share at most one vertex, then the vertices of $G$ can be
Externí odkaz:
http://arxiv.org/abs/2103.00875