论文标题
针对分数色数的新特征值绑定
New Eigenvalue Bound for the Fractional Chromatic Number
论文作者
论文摘要
给定图$ g $，我们让$ s^+（g）$表示$ g $的邻接矩阵正征值的正方形总和，我们类似地定义了$ s^ - （g）$。我们证明了这一点 \ [χ_f（g）\ ge 1+ \ max \左\ {\ frac {s^+（g）} {s^ - （g）}，\ frac {s^ - （g）} {s^+（g）} \（g）} \ right \} \} \ right \} \]，从而增强了相同的ando and ando和lin $ und und und ungant，n and and y n off and and $ chrout $ chr. 实际上，我们显示出更强的结果，即只要$ g $都具有$ g $ $ g $和$ h $的特征值，我们对边缘传输图$ h $进行限制。我们的证明利用了协会计划激励的想法。
Given a graph $G$, we let $s^+(G)$ denote the sum of the squares of the positive eigenvalues of the adjacency matrix of $G$, and we similarly define $s^-(G)$. We prove that \[χ_f(G)\ge 1+\max\left\{\frac{s^+(G)}{s^-(G)},\frac{s^-(G)}{s^+(G)}\right\}\] and thus strengthen a result of Ando and Lin, who showed the same lower bound for the chromatic number $χ(G)$. We in fact show a stronger result wherein we give a bound using the eigenvalues of $G$ and $H$ whenever $G$ has a homomorphism to an edge-transitive graph $H$. Our proof utilizes ideas motivated by association schemes.
