A hereditary property R of graphs is said to be reducible if there exist hereditary properties P1,P2 such that G ∈ R if and only if the set of vertices of G can be partitioned into V (G) = V1 ∪ V2 so that 〈V1〉 ∈ P1 and 〈V2〉 ∈ P2. The problem of the factorization of reducible properties into irreducible factors is investigated.

Several new characterizations of strongly irresolvable topological spaces are found and precise relationships are noted between strong irresolvability, hereditary irresolvability, and submaximality. It is noted that strong irresolvablity is a faint topological property, while neither hereditary irresolvablity nor submaximality are semitopological.

Recently, Bacsó and Tuza gave a full characterization of the graphs for which every connected induced subgraph has a connected dominating subgraph satisfying an arbitrary prescribed hereditary property. Using their result, we derive a similar characterization of the graphs for which any isolate-free induced subgraph has a total dominating subgraph that satisfies a prescribed additive hereditary...

In this article I will analyze the impact of forcing with a measure algebra on various topological statements. In particular our interest will focus on the study of hereditary separability and the hereditary Lindelöf property in the classes of compact, extremally disconnected, and cometrizable spaces.

Recently, Chakrabarty et al. [5] initiated a systematic study of capacitated set cover problems, and considered the question of how their approximability relates to that of the uncapacitated problem on the same underlying set system. Here, we investigate this connection further and give several results, both positive and negative. In particular, we show that if the underlying set system satisfi...

The edit distance between two graphs on the same labeled vertex set is the symmetric difference of the edge sets. The distance between a graph, G, and a hereditary property, H, is the minimum of the distance between G and each G′ ∈ H. The edit distance function of H is a function of p ∈ [0, 1] and is the limit of the maximum normalized distance between a graph of density p and H. This paper dev...

We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. W...