I am reading Graph Theory by Bondy and Murty. I always see the notation for a complete $k$-partite graph, but what is the notation for a $k$-partite graph? For example, my partite sets are of order $2$, $3$, and $4$, and it is not a complete $k$-partite graph. How can I write this graph?
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$\begingroup$I think you can just say "$3$-partite graph" or "tripartite graph", omitting the word "complete". "Bipartite graph" is certainly standard.
I assume that when you say
my partite sets are of order $2$, $3$, and $4$
you mean a graph with $9$ vertices, $2$ red, $3$ blue and $4$ yellow, all of whose edges connect vertices of different colors.
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