arXiv Open Access 2013

Internal Partitions of Regular Graphs

Amir Ban Nati Linial

Lihat Sumber

Abstrak

An internal partition of an $n$-vertex graph $G=(V,E)$ is a partition of $V$ such that every vertex has at least as many neighbors in its own part as in the other part. It has been conjectured that every $d$-regular graph with $n>N(d)$ vertices has an internal partition. Here we prove this for $d=6$. The case $d=n-4$ is of particular interest and leads to interesting new open problems on cubic graphs. We also provide new lower bounds on $N(d)$ and find new families of graphs with no internal partitions. Weighted versions of these problems are considered as well.

Topik & Kata Kunci

math.CO

Penulis (2)

Amir Ban

Nati Linial

Format Sitasi

APA MLA BibTeX

Ban, A., Linial, N. (2013). Internal Partitions of Regular Graphs. https://arxiv.org/abs/1307.5246

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2013
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓