# Chenqi Mou: *Chordal graphs in ordinary differential triangular decomposition in top-down style*

In this talk I will present some underlying connections between symbolic computation and graph theory. To be specific, we apply chordal graphs to study whether algorithms for computing triangular decomposition of ordinary differential polynomial sets preserve the chordal structures of the input polynomial sets. We first propose the concept of differential associated graph of an ordinary differential polynomial set, and then for two typical algorithms in top-down style for ordinary differential triangular decomposition based on the pseudo-division and subresultant regular subchain respectively, we prove that when the input differential polynomial set has a chordal differential associated graph G and one perfect elimination ordering of G is used, the differential associated graph of any polynomial set in the decomposition process by these two algorithms is a subgraph of G.