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pro vyhledávání: '"05c69"'
Diestel, Hundertmark and Lemanczyk asked whether every $k$-tangle in a graph is induced by a set of vertices by majority vote. We reduce their question to graphs whose size is bounded by a function in $k$. Additionally, we show that if for any fixed
Externí odkaz:
http://arxiv.org/abs/2411.13656
Autor:
Levit, Vadim E., Mandrescu, Eugen
Let $\alpha(G)$ denote the cardinality of a maximum independent set and $\mu(G)$ be the size of a maximum matching of a graph $G=\left( V,E\right) $. If $\alpha(G)+\mu(G)=\left\vert V\right\vert $, then $G$ is a K\"{o}nig-Egerv\'{a}ry graph, and $G$
Externí odkaz:
http://arxiv.org/abs/2411.12863
This article discusses $\Delta$-convexity on simple connected graphs. We establish general bounds for the Helly number, Radon number, and rank with respect to $\Delta$-convexity on graphs. Additionally, we give the exact values for the Helly number a
Externí odkaz:
http://arxiv.org/abs/2411.10816
Autor:
Taylan, Demet
We provide lower bounds on the connectivity of the independence complexes of hypergraphs. Additionally, we compute the homotopy types of the independence complexes of $d$-uniform properly-connected triangulated hypergraphs.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2411.10365
Autor:
Cançado, Frederico, Coutinho, Gabriel
Whenever graphs admit equitable partitions, their quotient graphs highlight the structure evidenced by the partition. It is therefore very natural to ask what can be said about two graphs that have the same quotient according to certain equitable par
Externí odkaz:
http://arxiv.org/abs/2411.09157
Networks are designed to communicate, operate and allocate the tasks to the respective commodities. Operating the supercomputers became challenging, and it was handled by the network design commonly known as hypercube, denoted by $Q^n$. In a recent s
Externí odkaz:
http://arxiv.org/abs/2411.06900
Autor:
Blázsik, Zoltán L., Nagy, Leila Vivien
In a directed graph $D$, a vertex subset $S\subseteq V$ is a total dominating set if every vertex of $D$ has an in-neighbor from $S$. A total dominating set exists if and only if every vertex has at least one in-neighbor. We call the orientation of s
Externí odkaz:
http://arxiv.org/abs/2411.04560
Let $G$ be a simple connected graph. If every pendant path in $G$ is at least $P_s$, we denote that $G\in \mathbb{G}_s$. For $G \in \mathbb{G}_s$, let $Q_s(G)$ be the set of vertices in $G$ that are distance $s$ from the pendant vertex, and let $|Q_s
Externí odkaz:
http://arxiv.org/abs/2411.04770
Let $G$ be a graph and $k \geq 3$ an integer. A subset $D \subseteq V(G)$ is a $k$-clique (resp., cycle) isolating set of $G$ if $G-N[D]$ contains no $k$-clique (resp., cycle). In this paper, we prove that every connected graph with maximum degree at
Externí odkaz:
http://arxiv.org/abs/2411.03666
A dominating set $D_{f}\subseteq V(G)$ of vertices in a graph $G$ is called a \emph{dom-forcing set} if the sub-graph induced by $\langle D_{f} \rangle$ must form a zero forcing set. The minimum cardinality of such a set is known as the dom-forcing n
Externí odkaz:
http://arxiv.org/abs/2411.00580