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 2016 · math.COShow all

2 papers · 2 filters

math.CO2016

Nordhaus-Gaddum and other bounds for the sum of squares of the positive eigenvalues of a graph

Clive Elphick, Mustapha Aouchiche

Terpai [22] proved the Nordhaus-Gaddum bound that $μ (G) + μ (G) \leq 4 n /3 - 1$ , where $μ (G)$ is the spectral radius of a graph $G$ with $n$ vertices. Let $s^{+}$ denote the…

math.CO2016

An inertial lower bound for the chromatic number of a graph

Clive Elphick, Pawel Wocjan

Let $χ (G$ ) and $χ_{f} (G)$ denote the chromatic and fractional chromatic numbers of a graph $G$ , and let $(n^{+}, n^{0}, n^{-})$ denote the inertia of $G$ . We prove that: \[ 1 + \max\left…