Let G be a graph and let D be a subset of its vertex set. D is called k-dominating if| N (v)∩
D|≥ k for all v∈ V (G)∖ D; D is called k-tuple dominating if| N v∩ D|≥ k for all v∈ V (G); and …

For a positive integer k, a subset S of vertices of a graph G is k-independent if each vertex in
S has at most k− 1 neighbors in S. We consider k-independent sets in two graph products …

Mixed domination and $2$-independence in trees Page 1 http://www.aimspress.com/journal/Math
AIMS Mathematics, 5(6): 5564–5571. DOI:10.3934/math.2020357 Received: 27 April 2020 …

A graph $ G $ is $ q $-Ramsey for another graph $ H $ if in any $ q $-edge-colouring of $ G
$ there is a monochromatic copy of $ H $, and the classic Ramsey problem asks for the …

For an integer, ak‐path vertex cover of a graph is a set that shares a vertex with every path
subgraph of order k in G. The minimum cardinality of ak‐path vertex cover is denoted by. We …

A graph G is said to be q-Ramsey for a graph H if for every q-colouring of the edges of H
there exists a monochromatic copy of H. Moreover, G is said to be minimal q-Ramsey for H if …

For a fixed positive integer k, a set S of vertices of a graph or multigraph is called a k-
independent set if the subgraph induced by S has maximum degree less than k. The well …

Abstract Let H=(V, E) be an s-uniform hypergraph of order n and k≥ 0 be an integer. A k-
independent set S⊆ V is a set of vertices such that the maximum degree in the hypergraph …