# Peter Dinkelacker's scientific contributions

**What is this page?**

This page lists the scientific contributions of an author, who either does not have a ResearchGate profile, or has not yet added these contributions to their profile.

It was automatically created by ResearchGate to create a record of this author's body of work. We create such pages to advance our goal of creating and maintaining the most comprehensive scientific repository possible. In doing so, we process publicly available (personal) data relating to the author as a member of the scientific community.

If you're a ResearchGate member, you can follow this page to keep up with this author's work.

If you are this author, and you don't want us to display this page anymore, please let us know.

It was automatically created by ResearchGate to create a record of this author's body of work. We create such pages to advance our goal of creating and maintaining the most comprehensive scientific repository possible. In doing so, we process publicly available (personal) data relating to the author as a member of the scientific community.

If you're a ResearchGate member, you can follow this page to keep up with this author's work.

If you are this author, and you don't want us to display this page anymore, please let us know.

## Publications (9)

In 2010 it was proved that a 3-regular matchstick graph of girth 5 must consist at least of 30 vertices. The smallest known example consisted of 180 vertices. In this article we construct an example consisting of 54 vertices and prove its geometrical correctness.

In this article we proof the existence of 4-regular planar unit-distance graphs consisting only of unit triangles without additional triangles. It is shown that the smallest number of unit triangles is ≤ 6422.

In 2010 it was proved that a 3-regular matchstick graph of girth 5 must consist at least of 30 vertices. The smallest known example consisted of 180 vertices. In this article we construct an example consisting of 54 vertices and prove its geometrical correctness.

In 2010 it was proved that a 3-regular matchstick graph of girth 5 must consist at least of 30 vertices. The smallest known example consisted of 180 vertices. In this article we construct an example consisting of 54 vertices and prove its geometrical correctness.

In this article we proof the existence of 4-regular planar unit-distance graphs consisting only of unit triangles without additional triangles. It is shown that the smallest number of unit triangles is $\leq$6422.

In this article we proof the existence of 4-regular planar unit-distance graphs consisting only of unit triangles without additional triangles. It is shown that the smallest number of unit triangles is ≤ 6422.

A matchstick graph is a graph drawn with straight edges in the plane such that the edges have unit length, and non-adjacent edges do not intersect. We call a matchstick graph (m; n)-regular if every vertex has only degree m or n. In this article the authors present the latest known (4; n)-regular matchstick graphs for 4 ≤ n ≤ 11 with a minimum numb...

A matchstick graph is a planar unit-distance graph. That is a graph drawn with straight edges in the plane such that the edges have unit length, and non-adjacent edges do not intersect. We call a matchstick graph 4-regular if every vertex has only degree 4. Examples of 4-regular matchstick graphs with less than 63 vertices are only known for 52, 54...

A matchstick graph is a graph drawn with straight edges in the plane such that the edges have unit length, and non-adjacent edges do not intersect. We call a matchstick graph (m; n)-regular if every vertex has only degree m or n. In this article we present the latest known (4; n)-regular matchstick graphs for 4 ≤ n ≤ 11 with a minimum number of ver...

## Citations

... For 52, 54, 57, 60, and 64 vertices only one example is known. For a proof we refer the reader to [5]. An overview of the currently known examples with 63 -70 vertices can be found in [3]. ...

... Proof. The results for d = 1 can be found in [11] and [12]. There are several possibilities to obtain 4-regular matchstick graphs of order n by combining examples of lower orders (see Figure 14). ...