Zobrazeno 1 - 10
of 2 565 978
pro vyhledávání: '"K. n."'
We discuss $(K,N)$-convexity and gradient flows for $(K,N)$-convex functionals on metric spaces, in the case of real $K$ and negative $N$. In this generality, it is necessary to consider functionals unbounded from below and/or above, possibly attaini
Externí odkaz:
http://arxiv.org/abs/2412.04574
Autor:
Herrman, Rebekah, Wisdom, Grace
Zero forcing is a process on a graph $G = (V,E)$ in which a set of initially colored vertices,$B_0(G) \subset V(G)$, can color their neighbors according to the color change rule. The color change rule states that if a vertex $v$ can color a neighbor
Externí odkaz:
http://arxiv.org/abs/2411.03178
Autor:
Cinkir, Zubeyir
We compute the total number of spanning trees for the generalized cone of the complete graph $K_n$ and a number of families of some modified bipartite graphs $K_{m,n}$. In particular, we obtain a new method of finding the number of spanning trees of
Externí odkaz:
http://arxiv.org/abs/2411.02874
Autor:
Kainen, Paul C.
A book embedding of the complete graph $K_n$ needs $\lceil \frac{n}{2} \rceil$ pages and the page-subgraphs can be chosen to be spanning paths (for $n$ even) and one spanning star for $n$ odd. We show that all page-subgraphs can be chosen to be {\rm
Externí odkaz:
http://arxiv.org/abs/2412.00971
Autor:
Andronikos, Theodore
This article introduces a novel Quantum Secret Sharing scheme with $( k, n )$ threshold and endowed with verification capability. The new protocol exploits the power of entanglement and evolves in three phases. The primary novelty of the new protocol
Externí odkaz:
http://arxiv.org/abs/2410.18643
Autor:
Gong, Charles
Given any $r$-edge coloring of $K_{n,n}$, how large is the maximum (over all $r$ colors) sized monochromatic subgraph guaranteed to be? We give answers to this problem for $r \leq 8$, when $r$ is a perfect square, and when $r$ is one less than a perf
Externí odkaz:
http://arxiv.org/abs/2410.19076
Autor:
Bandyopadhyay, Debmalya, Lo, Allan
Let $K_n^{(k)}$ be the complete $k$-graph on $n$ vertices. A $k$-uniform tight cycle is a $k$-graph with its vertices cyclically ordered so that every $k$ consecutive vertices form an edge and any two consecutive edges share exactly $k-1$ vertices. A
Externí odkaz:
http://arxiv.org/abs/2408.17176
Autor:
Arkhipov, Pavel, Kolmogorov, Vladimir
The $k$-forest problem asks to find $k$ forests in a graph $G$ maximizing the number of edges in their union. We show how to solve this problem in $O(k^3 \min\{kn, m\} \log^2 n + k \cdot{\rm MAXFLOW}(m, m) \log n)$ time, breaking the $O_k(n^{3/2})$ c
Externí odkaz:
http://arxiv.org/abs/2409.20314
Autor:
Zamora, Sergio, Zhu, Xingyu
For a polycyclic group $\Lambda$, $\text{rank} ( \Lambda )$ is defined as the number of $\mathbb{Z}$ factors in a polycyclic decomposition of $\Lambda$. For a finitely generated group $G$, $\text{rank} (G)$ is defined as the infimum of $ \text{rank}
Externí odkaz:
http://arxiv.org/abs/2406.10189