**Definition:**
A graph $G$ is chordal if every induced cycle in $G$ has length 3, and is co-chordal if the complement graph $G^c$ is chordal.The co-chordal
cover number, denoted $cochord (G)$, is the minimum number of co-chordal subgraphs required to cover the edges of $G$.


**Definition:** 
 Induced matching in a graph $G$ is a matching which forms an induced subgraph of $G$, and that $indmatch (G)$ denotes the number of edges in a largest induced matching.



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> Suppose $G$ is cycle .
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> 
> Is $cochord(G) \leq indmatch(G)+1$ true?
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> 
> 



Induced matching of cycle
**Yes.** Let $C\_n$ be the cycle on $n$ vertices. The size of a largest induced matching in $C\_n$ is exactly $\lfloor \frac{n}{3} \rfloor$, since we can take at most every third edge of $C\_n$. On the other hand, since $K\_n$ minus a $3$-edge path is chordal, we have $cochord(C\_n) \leq \lceil \frac{n}{3} \rceil$. Thus, $cochord(C\_n) \leq indmatch(C\_n)+1$, as required. 


