Zobrazeno 1 - 10
of 2 951
pro vyhledávání: '"05C69"'
Publikováno v:
Comp. Appl. Math. 41, 424 (2022)
A vertex subset S of a graph G is said to 2-dominate the graph if each vertex not in S has at least two neighbors in it. As usual, the associated parameter is the minimum cardinal of a 2-dominating set, which is called the 2-domination number of the
Externí odkaz:
http://arxiv.org/abs/2409.16703
Autor:
DeVivo, Zachary, Hladky, Robert K.
We briefly review known results on upper bounds for the minimal domination number $\gamma_n$ of a hypercube of dimension $n$, then present a new method for constructing dominating sets. Write $n =2^{\hat{n}}-1 +{\check{n}}$ with $0\leq {\check{n}}<2^
Externí odkaz:
http://arxiv.org/abs/2409.14621
Autor:
Long, Eoin, Ploscaru, Laurentiu
Given an $n$-vertex graph $G$, let $\hom (G)$ denote the size of a largest homogeneous set in $G$ and let $f(G)$ denote the maximal number of distinct degrees appearing in an induced subgraph of $G$. The relationship between these parameters has been
Externí odkaz:
http://arxiv.org/abs/2409.14134
Let $\mathscr{B}_n = \{ \pm x_1, \pm x_2, \pm x_3, \cdots, \pm x_{n-1}, x_n \}$ where $n>1$ is fixed, $x_i \in \mathbb{R}^+$, $i = 1, 2, 3, \cdots, n$ and $x_1 < x_2 < x_3 < \cdots < x_n$. Let $\phi(\mathscr{B}_n)$ be the set of all non-empty subsets
Externí odkaz:
http://arxiv.org/abs/2409.09317
Let $\mathcal{H}$ be a graph class and $k\in\mathbb{N}$. We say a graph $G$ admits a \emph{$k$-identification to $\mathcal{H}$} if there is a partition $\mathcal{P}$ of some set $X\subseteq V(G)$ of size at most $k$ such that after identifying each p
Externí odkaz:
http://arxiv.org/abs/2409.08883
Two relationships between the injective chromatic number and, respectively, chromatic number and chromatic index, are proved. They are applied to determine the injective chromatic number of Sierpi\'nski graphs and to give a short proof that Sierpi\'n
Externí odkaz:
http://arxiv.org/abs/2409.08856
The concept of zero forcing involves a dynamic coloring process by which blue vertices cause white vertices to become blue, with the goal of forcing the entire graph blue while choosing as few as possible vertices to be initially blue. Past research
Externí odkaz:
http://arxiv.org/abs/2409.04717
Directed graphs provide more subtle and precise modelling tools for optimization in road networks than simple graphs. In particular, they are more suitable in the context of alternative fuel vehicles and new automotive technologies, like electric veh
Externí odkaz:
http://arxiv.org/abs/2409.04226
Let $G$ be a $\mathbf{W}_{p}$ graph if $n\geq p$ and every $p$ pairwise disjoint independent sets of $G$ are contained within $p$ pairwise disjoint maximum independent sets. In this paper, we establish that every $\mathbf{W}_{p}$ graph $G$ is $p$-qua
Externí odkaz:
http://arxiv.org/abs/2409.00827
Autor:
Gözüpek, Didem, Peterin, Iztok
A map $c:V(G)\rightarrow\{1,\dots,k\}$ of a graph $G$ is a packing $k$-coloring if every two different vertices of the same color $i\in \{1,\dots,k\}$ are at distance more than $i$. The packing chromatic number $\chi_{\rho}(G)$ of $G$ is the smallest
Externí odkaz:
http://arxiv.org/abs/2409.00697