C. Elphick

activity

20122026

most citedUpper bounds for the achromatic and coloring numbers of a graph

2 citations · 13 across the 20 of their papers we have counts for

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Showing 2025Show all

4 papers · 1 filter

math.CO2025

Proof of a conjectured spectral upper bound on the chromatic number of a graph

Quanyu Tang, Clive Elphick

Let $G$ be a simple graph on $n$ vertices and $m$ edges with chromatic number $χ$ , and let $λ_{n}$ denote the least adjacency eigenvalue. Solving a conjecture of Fan, Yu and Wang~[El…

math.CO2025

A new conjecture on the inertia of graphs

Saieed Akbari, Clive Elphick, Hitesh Kumar +2

Let $G$ be a graph with adjacency matrix $A (G)$ . We conjecture that \[2n^+(G) \le n^-(G)(n^-(G) + 1),\] where $n^{+} (G)$ and $n^{-} (G)$ denote the number of positive and negative eigen…

math.CO2025

Inertia, Independence and Expanders

Quanyu Tang, Shengtong Zhang, Clive Elphick

Let $G$ be a graph on $n$ vertices, independence number $α (G)$ , Lovász theta function $ϑ (G)$ , and Shannon capacity $Θ (G)$ . We define $n_{\geq 0} (G)$ to be the minimum number…

math.CO2025

A Spectral Lower Bound on Chromatic Numbers using $p$ -Energy

Clive Elphick, Quanyu Tang, Shengtong Zhang

Let $A_{G}$ be the adjacency matrix of a simple graph $G$ , and let $χ (G)$ , $χ_{f} (G)$ , $χ_{q} (G)$ , $ξ (G)$ and $ξ_{f} (G)$ denote its chromatic number, fractional chromatic numb…

Proof of a conjectured spectral upper bound on the chromatic number of a graph

A new conjecture on the inertia of graphs

Inertia, Independence and Expanders

A Spectral Lower Bound on Chromatic Numbers using p-Energy

A Spectral Lower Bound on Chromatic Numbers using $p$ -Energy