If D is a digraph, then K∈V(D) is a quasi-kernel of D if D[K]is discrete and for each y∈V(D)-K there is x∈K such that the directed distance from y to x is less than three. We give formulae for the number of quasi-k...If D is a digraph, then K∈V(D) is a quasi-kernel of D if D[K]is discrete and for each y∈V(D)-K there is x∈K such that the directed distance from y to x is less than three. We give formulae for the number of quasi-kernels and for the number of minimal quasi-kernels of oriented paths and cycles.展开更多
The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z<sub>p</sub> for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we ...The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z<sub>p</sub> for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.展开更多
文摘If D is a digraph, then K∈V(D) is a quasi-kernel of D if D[K]is discrete and for each y∈V(D)-K there is x∈K such that the directed distance from y to x is less than three. We give formulae for the number of quasi-kernels and for the number of minimal quasi-kernels of oriented paths and cycles.
文摘The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z<sub>p</sub> for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.
