Wyniki wyszukiwania

1

Secure sets and their expansion in cubic graphs

100%

Jesse-Józefczyk K., Sidorowicz E.

Open Mathematics

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2014

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tom 12

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nr 11

1664-1673

EN

Consider a graph whose vertices play the role of members of the opposing groups. The edge between two vertices means that these vertices may defend or attack each other. At one time, any attacker may attack only one vertex. Similarly, any defender fights for itself or helps exactly one of its neighbours. If we have a set of defenders that can repel any attack, then we say that the set is secure. Moreover, it is strong if it is also prepared for a raid of one additional foe who can strike anywhere. We show that almost any cubic graph of order n has a minimum strong secure set of cardinality less or equal to n/2 + 1. Moreover, we examine the possibility of an expansion of secure sets and strong secure sets.

2

A metric graph satisfying [...] w 4 1 = 1 $w_4^1 = 1$ that cannot be lifted to a curve satisfying [...] dim ⁡ ( W 4 1 ) = 1 $\dim \;(W_4^1 ) = 1$

61%

Coppens M.

Open Mathematics

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2016

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tom 14

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nr 1

1-12

EN

For all integers g ≥ 6 we prove the existence of a metric graph G with [...] w41=1$w_4^1 = 1$ such that G has Clifford index 2 and there is no tropical modification G′ of G such that there exists a finite harmonic morphism of degree 2 from G′ to a metric graph of genus 1. Those examples show that not all dimension theorems on the space classifying special linear systems for curves have immediate translation to the theory of divisors on metric graphs.

3

The subalgebra lattice of a finite algebra

37%

Pióro K.

Open Mathematics

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2014

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tom 12

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nr 7

1052-1108

EN

The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more general case of partial algebras. Moreover, we use connections between algebras and hypergraphs to solve these problems.

Ograniczanie wyników

3 Open Mathematics

1 Coppens M.

1 Jesse-Józefczyk K.

1 Pióro K.

1 Sidorowicz E.

1 2016

2 2014

Secure sets and their expansion in cubic graphs

A metric graph satisfying [...] w 4 1 = 1 $w_4^1 = 1$ that cannot be lifted to a curve satisfying [...] dim ⁡ ( W 4 1 ) = 1 $\dim \;(W_4^1 ) = 1$

The subalgebra lattice of a finite algebra