Total Domination in Partitioned Graphs
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For δ ≥ 2 and k ≥ 3 we prove f t (G; k) ≤ 11|V|/7 and this inequality is best possible.
for δ ≥ 3 we prove that f t (G; 2) ≤ (5/4 − 1/372)|V|. That inequality may not be best possible, but we conjecture that f t (G; 2) ≤ 7|V|/6 is.
for δ ≥ 3 we prove f t (G; k) ≤ 3|V|/2 and this inequality is best possible.
for δ ≥ 3 the inequality g t (G; k) ≤ 3|V|/4 holds and is best possible.
KeywordsTotal domination Partitions and Hypergraphs
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