The maximum number of pairwise edge disjoint forests of order five in the complete graph <mml:math alttext="$K_n $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:math>, and the minimum number of forests of order five whose union is <mml:math alttext="$K_n $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:math>, are determined.

International Journal of Mathematics and Mathematical Sciences

The packing and covering of the complete graph I: the forests of order five

Abstract

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