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Exact(38)
Let G be a split graph.
Every split graph is 2-clique colourable.
Any split graph is 2-clique-colourable by Lemma 1.
A split-indifference graph is a split graph that is also an indifference graph.
Every spider is a split graph and therefore it is 2-clique-colourable by Lemma 1.
Then the characteristic graph of G is also a split graph.
Similar(22)
Fully dynamic algorithms of the latter kind are known for split graphs [L.
The characterization described extends a corresponding result for split graphs by Kloks [27].
Ibarra, Fully dynamic algorithms for chordal graphs and split graphs, Technical Report DCS-262-IR, University of Victoria, Canada, 2000].
This is a well-known NP-complete decision problem, open for several graph classes, including split graphs.
At the end of the paper, we show that the mixed domination problem is NP-complete even when restricted to split graphs, a subclass of chordal graphs.
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