2 citations · 4 across the 8 of their papers we have counts for
5 papers · 1 filter
Subgraph-universal planar graphs for trees
Helena Bergold, Vesna Iršič, Robert Lauff +3
We show that there exists an outerplanar graph on vertices for that contains every tree on vertices as a subgraph. This exten…
On the Uncrossed Number of Graphs
Martin Balko, Petr Hliněný, Tomáš Masařík +3
Visualizing a graph in the plane nicely, for example, without crossings, is unfortunately not always possible. To address this problem, Masařík and Hliněný [GD 2023] recently a…
Towards Crossing-Free Hamiltonian Cycles in Simple Drawings of Complete Graphs
Oswin Aichholzer, Joachim Orthaber, Birgit Vogtenhuber
It is a longstanding conjecture that every simple drawing of a complete graph on vertices contains a crossing-free Hamiltonian cycle. We strengthen this conjecture to "t…
Edge Partitions of Complete Geometric Graphs (Part 2)
Oswin Aichholzer, Johannes Obenaus, Joachim Orthaber +5
Recently, the second and third author showed that complete geometric graphs on vertices in general cannot be partitioned into plane spanning trees. Building up on this wor…
Edge Partitions of Complete Geometric Graphs (Part 1)
Johannes Obenaus, Joachim Orthaber
In this paper, we disprove the long-standing conjecture that any complete geometric graph on vertices can be partitioned into plane spanning trees. Our construction is bas…