Zobrazeno 1 - 10
of 72 346
pro vyhledávání: '"computer science and mathematics"'
The functionality of a graph $G$ is the minimum number $k$ such that in every induced subgraph of $G$ there exists a vertex whose neighbourhood is uniquely determined by the neighborhoods of at most $k$ other vertices in the subgraph. The functionali
Externí odkaz:
http://arxiv.org/abs/2412.19771
Boolean combinations allow combining given combinatorial objects to obtain new, potentially more complicated, objects. In this paper, we initiate a systematic study of this idea applied to graphs. In order to understand expressive power and limitatio
Externí odkaz:
http://arxiv.org/abs/2412.19551
Autor:
Pak, Igor, Robichaux, Colleen
Schubert coefficients $c_{u,v}^w$ are structure constants describing multiplication of Schubert polynomials. Deciding positivity of Schubert coefficients is a major open problem in Algebraic Combinatorics. We prove a positive rule for this problem ba
Externí odkaz:
http://arxiv.org/abs/2412.18984
Theoretical guarantees for double spending probabilities for the Nakamoto consensus under the $k$-deep confirmation rule have been extensively studied for zero/bounded network delays and fixed mining rates. In this paper, we introduce a ruin-theoreti
Externí odkaz:
http://arxiv.org/abs/2412.18599
Let $B$ be a set of Eulerian subgraphs of a graph $G$. We say $B$ forms a $k$-basis if it is a minimum set that generates the cycle space of $G$, and any edge of $G$ lies in at most $k$ members of $B$. The basis number of a graph $G$, denoted by $b(G
Externí odkaz:
http://arxiv.org/abs/2412.18595
Hard combinatorial optimization problems, often mapped to Ising models, promise potential solutions with quantum advantage but are constrained by limited qubit counts in near-term devices. We present an innovative quantum-inspired framework that dyna
Externí odkaz:
http://arxiv.org/abs/2412.18571