Yan Yang

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math.CO2026

On derivatives and higher-order derivatives of chromatic polynomials

Bo Ning, Yan Yang

Let $ G $ be a graph of order $ n $ with maximum degree $I^$ , and let $P (G, x)$ denote its chromatic polynomial. We investigate several properties of $P (G, x)$ related to its der…

math.CO2026

On a conjecture concerning the property of chromatic polynomials with negative variables

Yan Yang

Let $G$ be a graph of order $n$ and $P (G, x)$ be the chromatic polynomial of $G$ . Dong, Ge, Gong, Ning, Ouyang, and Tay (J. Graph Theory 96(2021) 343) conjectured that $\frac{d^k}{d…

math.CO2024

Counterexamples to two conjectures on mean color numbers of graphs

Wushuang Zhai, Yan Yang

The mean color number of an $n$ -vertex graph $G$ , denoted by $I^¼ (G)$ , is the average number of colors used in all proper $n$ -colorings of $G$ . For any graph $G$ and a vertex $w$ in…