Flip Graphs of Bounded-Degree Triangulations

Flip Graphs of Degree-Bounded (Pseudo-)Triangulations⋆

We study flip graphs of (pseudo-)triangulations whose maximum vertex degree is bounded by a constant k. In particular, we consider (pseudo-)triangulations of sets of n points in convex position in the plane and prove that their flip graph is connected if and only if k > 6; the diameter of the flip graph is O(n). We also show that for general point sets flip graphs of minimum pseudo-triangulatio...

Flip Graphs of Bounded-Degree Triangulations

We study flip graphs of triangulations whose maximum vertex degree is bounded by a constant k. In particular, we consider triangulations of sets of n points in convex position in the plane and prove that their flip graph is connected if and only if k > 6; the diameter of the flip graph is O(n). We also show that, for general point sets, flip graphs of pointed pseudo-triangulations can be discon...

k-forested choosability of graphs with bounded maximum average degree

A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...

Diamond Triangulations Contain Spanners of Bounded Degree

Given a triangulation G, whose vertex set V is a set of n points in the plane, and given a real number γ with 0 < γ < π, we design an O(n)-time algorithm that constructs a connected spanning subgraph G′ of G whose maximum degree is at most 14 + d2π/γe. If G is the Delaunay triangulation of V , and γ = 2π/3, we show that G′ is a t-spanner of V (for some constant t) with maximum degree at most 17...

Spanners of bounded degree graphs