论文标题
mod $ k $彩色索引索引为$ o（k）$
The mod $k$ chromatic index of graphs is $O(k)$
论文作者
论文摘要
令$χ'_k（g）$表示图形$ g $的边缘所需的最小颜色数，以每种颜色边缘跨越的子图的方式都具有$ 1 \ pmod k $的所有学位。 Scott [{\ em离散数学。 175}, 1-3 (1997), 289--291] proved that $χ'_k(G)\leq5k^2\log k$, and thus settled a question of Pyber [{\em Sets, graphs and numbers} (1992), pp. 583--610], who had asked whether $χ_k'(G)$ can be bounded solely as a function of $k$.我们证明$χ'_k（g）= o（k）$，肯定地回答了斯科特的问题。
Let $χ'_k(G)$ denote the minimum number of colors needed to color the edges of a graph $G$ in a way that the subgraph spanned by the edges of each color has all degrees congruent to $1 \pmod k$. Scott [{\em Discrete Math. 175}, 1-3 (1997), 289--291] proved that $χ'_k(G)\leq5k^2\log k$, and thus settled a question of Pyber [{\em Sets, graphs and numbers} (1992), pp. 583--610], who had asked whether $χ_k'(G)$ can be bounded solely as a function of $k$. We prove that $χ'_k(G)=O(k)$, answering affirmatively a question of Scott.
