Abstract We consider maximum properly edge-colored trees in edge-colored graphs Gc. We also consider the problem where, given a vertex r, determine whether the graph has a spanning tree rooted at r, such that all root-to-leaf paths are properly colored. We consider these problems from graphtheoretic as well as algorithmic viewpoints. We prove their optimization versions to be NP-hard in general...

Let G be a planar graph with n vertices whose vertex set is partitioned into subsets V0, . . . , Vk−1 for some positive integer 1 ≤ k ≤ n and let S be a set of n distinct points in the plane partitioned into subsets S0, . . . , Sk−1 with |Vi| = |Si| (0 ≤ i ≤ k − 1). This paper studies the problem of computing a crossing-free drawing of G such that each vertex of Vi is mapped to a distinct point...

This paper examines the use of market-share thresholds (safe harbors) in evaluating whether a given vertical practice should be challenged. Such thresholds are typically found in vertical restraints guidelines (e.g., the 2000 Guidelines for the European Commission and the 1985 Guidelines for the U.S. Department of Justice). We consider a model of resale price maintenance (RPM) in which firms em...

relative diffuse reflection measurements from the original and ground surfaces using a he-ne laser are reported. the intensity measurements for the metallic, transparent dielectric, matte plastic surfaces and colored papers are presented. our results indicate that among metallic surfaces tested, aluminum has the highest diffuse reflectance; while the original stainless steel surface shows the l...

It is shown that in the SU(2) Yang Mills Higgs theory with broken gauge symmetry a flux tube solution filled with a color longitudinal electric field exists. The origin of the gauge symmetry breakdown for this case is discussed.