PreprintCC BY 4.0arXiv
A General Inequality for Walks in Graphs
Abstract
Let G be a graph and wk(G) denote the number of walks in G of length k. For sequences a1, ⋯, an and b1, ⋯, bn of non-negative integers such that a1 + ⋯ + an = b1 + ⋯ + bn, we determine a simple necessary and sufficient condition on a1, ⋯, an, b1, ⋯, bn for the inequality wa1(G) ⋯ wan(G) ≥ wb1(G) ⋯ wbn(G) to hold for any graph G.
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BibTeX
@misc{wilson2026general,
title = {{A General Inequality for Walks in Graphs}},
author = {Chase Wilson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11846},
eprint = {2609.11846},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11846},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A General Inequality for Walks in Graphs
AU - Chase Wilson
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11846
UR - https://arxiv.org/abs/2609.11846
AB - Let G be a graph and w_k(G) denote the number of walks in G of length k. For sequences a_1, ⋯, a_n and b_1, ⋯, b_n of non-negative integers such that a_1 + ⋯ + a_n = b_1 + ⋯ + b_n, we determine a simple necessary and sufficient condition on a_1, ⋯, a_n, b_1, ⋯, b_n for the inequality w_a_1(G) ⋯ w_a_n(G) ≥ w_b_1(G) ⋯ w_b_n(G) to hold for any graph G.
ER -