4 papers · 1 filter
Polylogarithmic Bounds for Nested Cycles without Geometric Crossings
Yue Xu, Jiasheng Zeng, Xiao-Dong Zhang
A problem of Erdős asks for extremal conditions forcing edge-disjoint cycles with a prescribed nested structure. In the geometric version, the nesting is required to be noncrossing…
Counting geodesic paths in graphs
Martin Knor, Jelena Sedlar, Riste Škrekovski +1
A geodesic is a shortest path which connects a pair of vertices of a graph G. In this paper we define the geodesic subpath number gpn(G) of a graph G as the number of geodesics in…
Localized Version of Hypergraph Erdos-Gallai Theorem
Kai Zhao, Xiao-Dong Zhang
This paper focuses on extensions of the classic Erdős-Gallai Theorem for the set of weighted function of each edge in a graph. The weighted function of an edge of an -vertex…
The Number of Subtrees of Trees with Given Degree Sequence
Xiu-Mei Zhang, Xiao-Dong Zhang, Daniel Gray +1
This paper investigates some properties of the number of subtrees of a tree with given degree sequence. These results are used to characterize trees with the given degree sequence…