Corpus ID: 174801873

# The average cut-rank of graphs

@article{Nguyen2019TheAC,
title={The average cut-rank of graphs},
author={Huy-Tung Nguyen and Sang-il Oum},
journal={arXiv: Combinatorics},
year={2019}
}
• Published 2019
• Mathematics
• arXiv: Combinatorics
• The cut-rank of a set $X$ of vertices in a graph $G$ is defined as the rank of the $\lvert X\rvert \times\lvert V(G)\setminus X\rvert$ $0$-$1$ matrix over the binary field whose $(i,j)$-entry is $1$ if and only if the $i$-th vertex in $X$ and the $j$-th vertex in $V(G)\setminus X$ are adjacent. We introduce the graph parameter called the average cut-rank of a graph, defined as the expected value of the cut-rank of a random set of vertices. We prove that graphs of bounded average cut-rank are… CONTINUE READING

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