Heather Guarnera

College of Wooster · Department of Mathematics and Computer Science

The [Formula presented]-hyperbolicity of a graph is defined by a simple 4-point condition: for any four vertices [Formula presented], [Formula presented], [Formula presented], and [Formula presented], the two larger of the distance sums [Formula presented], [Formula presented], and [Formula presented] differ by at most [Formula presented]. Hyperbol...

A graph $G = (V,E)$ is distance hereditary if every induced path of $G$ is a shortest path. In this paper, we show that the eccentricity function $e(v) = \max\{d(v, u) : u \in V \}$ in any distance-hereditary graph $G$ is almost unimodal, that is, every vertex $v$ with $e(v) > rad(G) + 1$ has a neighbor with smaller eccentricity. Here, $rad(G) = \m...

A graph G=(V,E) is δ-hyperbolic if for any four vertices u,v,w,x, the two larger of the three distance sums d(u,v)+d(w,x), d(u,w)+d(v,x), d(u,x)+d(v,w) differ by at most 2δ≥0. This paper describes the eccentricity terrain of a δ-hyperbolic graph. The eccentricity function eG(v)=max⁡{d(v,u):u∈V} partitions vertices of G into eccentricity layers Ck(G...

A graph is Helly if its disks satisfy the Helly property, i.e., every family of pairwise intersecting disks in G has a common intersection. It is known that for every graph G, there exists a unique smallest Helly graph H(G) into which G isometrically embeds; H(G) is called the injective hull of G. Motivated by this, we investigate the structural pr...

A new metric parameter for a graph, Helly-gap, is introduced. A graph $G$ is called $\alpha$-weakly-Helly if any system of pairwise intersecting disks in $G$ has a nonempty common intersection when the radius of each disk is increased by an additive value $\alpha$. The minimum $\alpha$ for which a graph $G$ is $\alpha$-weakly-Helly is called the He...

A graph is Helly if its disks satisfy the Helly property, i.e., every family of pairwise intersecting disks in G has a common intersection. It is known that for every graph G, there exists a unique smallest Helly graph \(\mathcal {H}(G)\) into which G isometrically embeds; \(\mathcal {H}(G)\) is called the injective hull of G. Motivated by this, we...

We investigate a metric parameter “Leanness” of graphs which is a formalization of a well-known Fellow Travelers Property present in some metric spaces. Given a graph \(G=(V,E)\), the leanness of G is the smallest \(\lambda \) such that, for every pair of vertices \(x,y\in V\), all shortest (x, y)-paths stay within distance \(\lambda \) from each o...

A graph is Helly if every family of pairwise intersecting balls has a nonempty common intersection. The class of Helly graphs is the discrete analogue of the class of hyperconvex metric spaces. It is also known that every graph isometrically embeds into a Helly graph, making the latter an important class of graphs in Metric Graph Theory. We study d...

A new metric parameter for a graph, Helly-gap, is introduced. A graph G is called α-weakly-Helly if any system of pairwise intersecting disks in G has a nonempty common intersection when the radius of each disk is increased by an additive value α. The minimum α for which a graph G is α-weakly-Helly is called the Helly-gap of G and denoted by α(G)....

A graph is Helly if every family of pairwise intersecting balls has a nonempty common intersection. The class of Helly graphs is the discrete analogue of the class of hyperconvex metric spaces. It is also known that every graph isometrically embeds into a Helly graph, making the latter an important class of graphs in Metric Graph Theory. We study d...

A graph G=(V,E) is distance hereditary if every induced path of G is a shortest path. In this paper, we show that the eccentricity function e(v)=max⁡{d(v,u):u∈V} in any distance-hereditary graph G is almost unimodal, that is, every vertex v with e(v)>rad(G)+1 has a neighbor with smaller eccentricity. Here, rad(G)=min⁡{e(v):v∈V} is the radius of gra...

A graph $G=(V,E)$ is $\delta$-hyperbolic if for any four vertices $u,v,w,x$, the two larger of the three distance sums $d(u,v)+d(w,x)$, $d(u,w)+d(v,x)$, and $d(u,x)+d(v,w)$ differ by at most $2\delta \geq 0$. Recent work shows that many real-world graphs have small hyperbolicity $\delta$. This paper describes the eccentricity terrain of a $\delta$-...

An approach to automatically recover the name of the branch where a given commit is originally made within a GitHub repository is presented and evaluated. This is a difficult task because in Git, the commit object does not store the name of the branch when it is created. Here this is termed the commit's branch of origin. Developers typically use br...