Hadwiger and Hajós conjectured that for every positive integer t, Kt+1-minor free graphs Kt+1-topological minor are properly t-colorable, respectively. Clustered coloring version of these two conjectures which only require monochromatic components to have bounded size has been extensively studied. In this paper we consider the clustered immersion-variant Hadwiger's Hajós' conjecture proposed by...

The problem of sequence and time-series segmentation has been discussed widely and it has been applied successfully in a variety of areas, including computational genomics, data analysis for scientific applications, and telecommunications. In many of these areas the sequences involved are multidimensional, and the goal of the segmentation is to discover sequence segments with small variability....