An Approximation Algorithm for the Maximum Induced Matching Problem on C₅-Free Regular Graphs

Abstract

In this paper, we investigate the maximum induced matching problem (MaxIM) on C₅-free d-regular graphs. The previously known best approximation ratio for MaxIM on C₅-free d-regular graphs is $\left(\frac{3d}{4}-\frac{1}{8}+\frac{3}{16d-8}\right)$. In this paper, we design a $\left(\frac{2d}{3}+\frac{1}{3}\right)$-approximation algorithm, whose approximation ratio is strictly smaller/better than the previous one when d≥6.