Scott proved in 1997 that for any tree T , every graph with bounded clique number which does not contain any subdivision of T as an induced subgraph has bounded chromatic number. Scott also conjectured that the same should hold if T is replaced by any graph H. Pawlik et al. recently constructed a family of trianglefree intersection graphs of segments in the plane with unbounded chromatic number...

Abstract. Predicting effective permeabilities of fractured rock masses is a crucial component reservoir modeling. Its often realized with the discrete fracture network (DFN) method, whereby single-phase incompressible fluid flow modeled in representations individual fractures network. Depending on overall number fractures, this can result high computational costs. Equivalent continuum models (E...

We show that for every graph $G$ and $H$ obtained by subdividing each edge of at least $\Omega(\log |V(G)|)$ times, is nonrepetitively 3-colorable. In fact, we \pi'(G))$ subdivisions per are enough, where $\pi'(G)$ the nonrepetitive chromatic index $G$. This answers a question Wood improves similar result Pezarski Zmarz stated existence one 3-colorable subdivision with linear number vertices ed...

A simple algorithm is provided for randomly sampling a set of N+1 weights such that their sum constrained to be equal one, analogous subdividing pie into slices where the probability distribution slice volumes are identically distributed. The cumulative density and functions random provided. algorithmic implementation number made available. This has potential applications in calibration, uncert...