Utku Okur

activity

20232026

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3 papers · 1 filter

math.CO2025

Multigraphs with Unique Partition into Cycles

Joshua Cooper, Utku Okur

Due to Veblen's Theorem, if a connected multigraph $X$ has even degrees at each vertex, then it is Eulerian and its edge set has a partition into cycles. In this paper, we show tha…

math.CO2025

Partitions of an Eulerian Digraph into Circuits

Joshua Cooper, Utku Okur

We investigate a cancellation property satisfied by a connected Eulerian digraph $D$ . Namely, unless $D$ is a single directed cycle, we have $\sum_{k \geq 1} (- 1)^{k} f_{k} (D) = 0$ , whe…

math.CO2025

Reconstruction of caterpillar tanglegrams

Ann Clifton, Eva Czabarka, Kevin Liu +4

A tanglegram consists of two rooted binary trees with the same number of leaves and a perfect matching between the leaves of the trees. Given a size- $n$ tanglegram, i.e., a tangleg…