Results 131 to 140 of about 349,803 (277)

Intersection Numbers of the Natural Embedding of the Twisted Triality Hexagon T ( q 3 , q ) ${\mathsf{T}}({q}^{3},q)$ in PG ( 7 , q 3 ) ${\mathsf{PG}}(7,{q}^{3})$

Journal of Combinatorial Designs, EarlyView.
ABSTRACT In this paper, we study and characterise the natural embedding of the twisted triality hexagon T ( q 3 , q ) ${\mathsf{T}}({q}^{3},q)$ in PG ( 7 , q 3 ) ${\mathsf{PG}}(7,{q}^{3})$. We begin by describing the possible intersections of subspaces of PG ( 7 , q 3 ) ${\mathsf{PG}}(7,{q}^{3})$ with T ( q 3 , q ) ${\mathsf{T}}({q}^{3},q)$.
Sebastian Petit, Geertrui Van de Voorde
wiley   +1 more source

On Kotzig's Perfect Set Problem of Hamiltonian Cycle Decompositions of the Complete Graph

Journal of Combinatorial Designs, EarlyView.
ABSTRACT A Hamiltonian cycle decomposition (HCD) of K n ${K}_{n}$ is a set of Hamiltonian cycles in which each 1‐path of K n ${K}_{n}$ appears exactly once. A Dudeney set of K n ${K}_{n}$ is a set of Hamiltonian cycles in which each 2‐path of K n ${K}_{n}$ appears exactly once.
Nobuaki Mutoh
wiley   +1 more source

ShZZaM

Proceedings of the International Florida Artificial Intelligence Research Society Conference
This paper describes ShZZaM, a tool that translates natural language to typed first-order logic, using Large Language Models (LLMs) and Automated Theorem Proving (ATP).
Geoff Sutcliffe, Danial Haroon
doaj  

Formal verification of bioinformatics software using model checking and theorem proving. [PDF]

Brief Bioinform
Weerasena H, Jayasena A, Boucher C, Mishra P.   +3 more
europepmc   +1 more source

R ( 5 , 5 ) ≤ 46 $R(5,5)\le 46$

Journal of Graph Theory, EarlyView.
ABSTRACT We prove that the Ramsey number R ( 5 , 5 ) $R(5,5)$ is less than or equal to 46. The proof uses a combination of linear programming and checking a large number of cases by computer. All of the computational parts of the proof were independently implemented by both authors, with consistent results.
Vigleik Angeltveit, Brendan D. McKay
wiley   +1 more source

Towards Characterization of Five‐List‐Colorability of Toroidal Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT Through computer‐assisted enumeration, we list minimal obstructions for 5‐choosability of graphs on the torus with the following additional property: There exists a cyclic system of non‐contractible triangles around the torus where the consecutive triangles are at distance at most four.
Zdeněk Dvořák, Félix Moreno Peñarrubia   +1 more
wiley   +1 more source

Disjoint Total Dominating Sets in Planar Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT The vertex set of any planar graph of minimum degree at least 3 can be colored in two colors so that every vertex has a neighbor of each color. If the graph is a planar triangulation, the coloring can be chosen such that every vertex has a neighbor of its own color and at least two neighbors of the opposite color.
Eva Rotenberg, Daniel Rutschmann, Carsten Thomassen   +2 more
wiley   +1 more source

On Strongly and Robustly Critical Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT In extremal combinatorics, it is common to focus on structures that are minimal with respect to a certain property. In particular, critical and list‐critical graphs occupy a prominent place in graph coloring theory. Stiebitz, Tuza, and Voigt introduced strongly critical graphs, i.e., graphs that are k $k$‐critical yet L $L$‐colorable with ...
Anton Bernshteyn, Hemanshu Kaul, Jeffrey A. Mudrock, Gunjan Sharma   +3 more
wiley   +1 more source