On the unit interval graphs which are paired k-disjoint path coverable

Abstract

In the research content of this paper, we characterize the unit interval graphs which are paired [Formula: see text]-disjoint path coverable. Specifically, we prove that [Formula: see text] is paired [Formula: see text]-disjoint path coverable if and only if [Formula: see text] is [Formula: see text]-connected, where [Formula: see text]. Moreover, we show that [Formula: see text] is semi-paired [Formula: see text]-disjoint path coverable if and only if [Formula: see text] is [Formula: see text]-connected where [Formula: see text] and [Formula: see text].