The problem of finite axiomatizability for strongly minimal graph theories

1989 ◽  
Vol 28 (3) ◽  
pp. 183-194 ◽  
Author(s):  
A. A. Ivanov
Keyword(s):  
Finite Axiomatizability ◽  
Minimal Graph

scholarly journals On Ramsey-Minimal Infinite Graphs

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Jordan Barrett ◽  
Valentino Vito
Keyword(s):  
Ramsey Theory ◽  
Infinite Graphs ◽  
Minimal Graph ◽  
Finite Graphs ◽  
Minimal Graphs ◽  
Finite Case ◽  
Ramsey Minimal Graph ◽  
General Conditions

For fixed finite graphs $G$, $H$, a common problem in Ramsey theory is to study graphs $F$ such that $F \to (G,H)$, i.e. every red-blue coloring of the edges of $F$ produces either a red $G$ or a blue $H$. We generalize this study to infinite graphs $G$, $H$; in particular, we want to determine if there is a minimal such $F$. This problem has strong connections to the study of self-embeddable graphs: infinite graphs which properly contain a copy of themselves. We prove some compactness results relating this problem to the finite case, then give some general conditions for a pair $(G,H)$ to have a Ramsey-minimal graph. We use these to prove, for example, that if $G=S_\infty$ is an infinite star and $H=nK_2$, $n \geqslant 1$ is a matching, then the pair $(S_\infty,nK_2)$ admits no Ramsey-minimal graphs.

scholarly journals On the Decidability of Intuitionistic Tense Logic without Disjunction

2020 ◽  
Author(s):  
Fei Liang ◽  
Zhe Lin
Keyword(s):  
Proof Theory ◽  
Tense Logic ◽  
Heyting Algebras ◽  
Finite Model ◽  
Algebraic Proof ◽  
Model Property ◽  
Algebraic Models ◽  
Finite Axiomatizability ◽  
Finite Model Property ◽  
Modal Operators

Implicative semi-lattices (also known as Brouwerian semi-lattices) are a generalization of Heyting algebras, and have been already well studied both from a logical and an algebraic perspective. In this paper, we consider the variety ISt of the expansions of implicative semi-lattices with tense modal operators, which are algebraic models of the disjunction-free fragment of intuitionistic tense logic. Using methods from algebraic proof theory, we show that the logic of tense implicative semi-lattices has the finite model property. Combining with the finite axiomatizability of the logic, it follows that the logic is decidable.

On the finite axiomatizability of ∀Σ̂1b(R̂21)

2018 ◽  
Vol 64 (1-2) ◽  
pp. 6-24
Author(s):  
Chris Pollett
Keyword(s):  
Finite Axiomatizability

Extension of Rescheduling Based on Minimal Graph Cut

2008 ◽  
pp. 340-351
Author(s):  
Marián Lekavý ◽  
Pavol Návrat
Keyword(s):  
Graph Cut ◽  
Minimal Graph

On the Non-Existence of a Type of Regular Graphs of Girth 5

1967 ◽  
Vol 19 ◽  
pp. 644-648 ◽  
Author(s):  
William G. Brown
Keyword(s):  
Lower Bound ◽  
Regular Graph ◽  
Regular Graphs ◽  
Minimal Graph ◽  
Image Position

ƒ(k, 5) is defined to be the smallest integer n for which there exists a regular graph of valency k and girth 5, having n vertices. In (3) it was shown that1.1Hoffman and Singleton proved in (4) that equality holds in the lower bound of (1.1) only for k = 2, 3, 7, and possibly 57. Robertson showed in (6) that ƒ(4, 5) = 19 and constructed the unique minimal graph.

Representation of competitions by complex neutrosophic information

2020 ◽  
Vol 39 (5) ◽  
pp. 7881-7897
Author(s):  
Saba Siddique ◽  
Uzma Ahmad ◽  
Wardat us Salam ◽  
Muhammad Akram ◽  
Florentin Smarandache
Keyword(s):  
Real Life ◽  
Minimal Graph ◽  
Research Article ◽  
Competition Graph ◽  
Proposed Model ◽  
Extended Approach ◽  
Generalized Complex ◽  
Neutrosophic Graph ◽  
Competition Number

The concept of generalized complex neutrosophic graph of type 1 is an extended approach of generalized neutrosophic graph of type 1. It is an effective model to handle inconsistent information of periodic nature. In this research article, we discuss certain notions, including isomorphism, competition graph, minimal graph and competition number corresponding to generalized complex neutrosophic graphs. Further, we describe these concepts by several examples and present some of their properties. Moreover, we analyze that a competition graph corresponding to a generalized complex neutrosophic graph can be represented by an adjacency matrix with suitable real life examples. Also, we enumerate the utility of generalized complex neutrosophic competition graphs for computing the strength of competition between the objects. Finally, we highlight the significance of our proposed model by comparative analysis with the already existing models.

scholarly journals Some results on finite axiomatizability in modal logic.

1965 ◽  
Vol 6 (4) ◽  
pp. 301-308 ◽  
Author(s):  
E. J. Lemmon
Keyword(s):  
Modal Logic ◽  
Finite Axiomatizability
Sign in / Sign up

Export Citation Format

Share Document