$\tau$-critical graphs

1 $\tau$-critical graphs

Here we study a graph class called $\tau$-critical graphs.

Definition 1. A graph $G$ is $\tau$-critical if for all proper subgraphs $G^{\prime }$ of $G$, where $\tau (\cdot )=n(\cdot )-\alpha (\cdot )$.

Source code for this project may be found in this Github repository.

More information on $\tau$-critical graphs may be found in [1].

2 Enumeration

All graphs are here listed in graph6 format for reference.

$\tau =1$	(1 graph)
$\tau =2$	(2 graphs)
$\tau =3$	(4 graphs)
$\tau =4$	(8 graphs)
$\tau =5$	(18 graphs)
$\tau =6$	(56 graphs)