Mycielskian graph M5.
The Mycielskian graph sequence generates graphs that are triangle-free
and with a known chromatic number (i.e. the minimum number of colors
required to color the vertices of the graph).
Known properties of this graph (M5) include the following:
* M5 has a minimum chromatic number of 5.
* M5 is triangle-free (i.e. no cycles of length 3 exist).
* M5 has a Hamiltonian cycle.
* M5 has a clique number of 2.
* M5 is factor-critical, meaning every subgraph of |V|-1 vertices has
a perfect matching.
Mycielski graphs were first described by Jan Mycielski in the following
publication:
Mycielski, J., 1955. Sur le coloriage des graphes. Colloq. Math.,
3: 161-162.