Zobrazeno 1 - 10
of 104
pro vyhledávání: '"ŠPACAPAN, SIMON"'
Autor:
Ai, Jiangdong, Ellingham, M. N., Gao, Zhipeng, Huang, Yixuan, Liu, Xiangzhou, Shan, Songling, Špacapan, Simon, Yue, Jun
Let $G$ be a graph (with multiple edges allowed) and let $T$ be a tree in $G$. We say that $T$ is $\textit{even}$ if every leaf of $T$ belongs to the same part of the bipartition of $T$, and that $T$ is $\textit{weakly even}$ if every leaf of $T$ tha
Externí odkaz:
http://arxiv.org/abs/2409.15522
A path factor in a graph $G$ is a factor of $G$ in which every component is a path on at least two vertices. Let $T\Box P_n$ be the Cartesian product of a tree $T$ and a path on $n$ vertices. Kao and Weng proved that $T\Box P_n$ is hamiltonian if $T$
Externí odkaz:
http://arxiv.org/abs/2408.06770
Autor:
Špacapan, Simon
Let $\gamma(G)$ denote the domination number of graph $G$. Let $G$ and $H$ be graphs and $G\Box H$ their Cartesian product. For $h\in V(H)$ define $G_h=\{(g,h)\,|\,g\in V(G)\}$ and call this set a $G$-layer of $G\Box H$. We prove the following specia
Externí odkaz:
http://arxiv.org/abs/2212.09571
Autor:
Špacapan, Simon
The prism over a graph $G$ is the Cartesian product of $G$ with the complete graph on two vertices. A graph $G$ is prism-hamiltonian if the prism over $G$ is hamiltonian. We prove that every polyhedral graph (i.e. 3-connected planar graph) of minimum
Externí odkaz:
http://arxiv.org/abs/2104.04266
Let $G$ and $H$ be graphs, and $G\boxtimes H$ the strong product of $G$ and $H$. We prove that for any connected graphs $G$ and $H$ there is a strongly connected orientation $D$ of $G\boxtimes H$ such that ${\rm diam}(D)\leq 2r+15$, where $r$ is the
Externí odkaz:
http://arxiv.org/abs/1909.12022
Autor:
Spacapan, Simon
The prism over a graph $G$ is the Cartesian product of $G$ with the complete graph $K_2$. A graph $G$ is hamiltonian if there exists a spanning cycle in $G$, and $G$ is prism-hamiltonian if the prism over $G$ is hamiltonian. In [M.~Rosenfeld, D.~Barn
Externí odkaz:
http://arxiv.org/abs/1906.06683
SEPARATION OF CARTESIAN PRODUCTS OF GRAPHS INTO SEVERAL CONNECTED COMPONENTS BY THE REMOVAL OF EDGES
Autor:
Špacapan, Simon
Publikováno v:
Applicable Analysis and Discrete Mathematics, 2021 Oct 01. 15(2), 357-377.
Externí odkaz:
https://www.jstor.org/stable/27090834
Autor:
Spacapan, Simon
We introduce a class of plane graphs called weak near-triangulations, and prove that this class is closed under certain graph operations. Then we use the properties of weak near-triangulations to prove that every plane triangulation on $n>6$ vertices
Externí odkaz:
http://arxiv.org/abs/1806.06932
Autor:
Erker Tjaša Paj, Špacapan Simon
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 42, Iss 3, Pp 905-920 (2022)
A set S ⊆ V (G) is a vertex k-cut in a graph G = (V (G), E(G)) if G − S has at least k connected components. The k-connectivity of G, denoted as κk(G), is the minimum cardinality of a vertex k-cut in G. We give several constructions of a set S s
Externí odkaz:
https://doaj.org/article/64ced7580e824859b251c143560162c0
Autor:
Špacapan, Simon
Publikováno v:
In Journal of Combinatorial Theory, Series B January 2021 146:364-371