[Nauty-list] Small Graphs

["Jos Ra. Portillo Fernández"]

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Hi all

I am trying to generate a lot of graphs. By example, I need all the
graphs of 17 vertices free of  K_2 + C_4, and verifying that all vertex
are included in a K_5 and minimum degree 5. These graphs cannot admit a
coloration green-red with the conditions: 1)  two vertices adjacents are
not green simultaneously and 2) in each subgraph K_5 there is exactly
one green vertex.

I hace used gtools for generate this graphs. I use a program (called
w5f) that call geng for obtain all the graphs of 17 vertices free of
K_2 + C_4 with minimum degree 5

> ./w5f -Cd5 17 > temp

After, I use pickg modified for the conditions of K_5 and coloring:

> ./pickg -WH temp > temp2

but this method is, obviously, inneficient.

Can you help me with any idea? i think that the condition of K_5 must be
computed simultaeously with the geng condition, but I have confused
about what code it in geng-nauty.

thanks (and sorry for my poor English)
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