# An analogue of the Whithey theorem for edge graphs of multigraphs, and edge multigraphs

```@inproceedings{Zverovich1997AnAO,
title={An analogue of the Whithey theorem for edge graphs of multigraphs, and edge multigraphs},
author={I. Zverovich},
year={1997}
}```
We deduce an analogue of the Whitney theorem for the edge graphs of multigraphs. We introduce and investigate edge multigraphs as well.
5 Citations
Line graphs of multigraphs and Hamilton-connectedness of claw-free graphs
• Mathematics, Computer Science
• J. Graph Theory
• 2011
A closure concept that turns a claw-free graph into the line graph of a multigraph while preserving its (non-)Hamilton-connectedness is introduced, and it is proved that the closure operation is, in a sense, best possible. Expand
On 1-Hamilton-connected claw-free graphs
• Mathematics, Computer Science
• Discret. Math.
• 2014
It is proved that (i)every 5-connected claw-free graph with minimum degree at least 6 is 1-Hamilton-connected, and (ii)every 4-connected claws-free hourglass-freegraph is 1 -hamiltonian. Expand
On Forbidden Pairs Implying Hamilton-Connectedness
• Mathematics, Computer Science
• J. Graph Theory
• 2013
It is shown that every 3-connected -free graph is Hamilton connected for and or N1, 2, 2 and the proof of this result uses a new closure technique developed by the third and fourth authors. Expand
InstaHide's Sample Complexity When Mixing Two Private Images
• Computer Science, Mathematics
• ArXiv
• 2020
It is shown that it suffices to use O(n_{\mathsf{priv}} - 2/(k-2/3) + 1) samples to recover one private image in O(k-1) time for any integer \$k, where n and n denote the number of images used in the private and the public dataset to generate a mixed image sample. Expand