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Degree conditions for the partition of a graph into triangles and quadrilaterals
degree partition triangle quadrilateral
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2011/3/1
For two positive integers r and s with r ≥ 2s−2, if G is a graph of order 3r+4s such that d(x)+d(y) ≥ 4r+4s for every xy 6∈ E(G), then G independently contains r triangles and s quadrilaterals, ...
An integration of Euler's pentagonal partition
Euler's pentagonal partition
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2010/12/8
A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler’s recurrence based on the penta...