Ear decompositions of graphs: an unexpected tool in combinatorial commutative algebra

Thời gian: 9h30, thứ 6, ngày 26/5/2023

Địa điểm: Hội trường Hoàng Tụy, Tầng 2, Nhà A6, Viện Toán học

Tóm tắt: An ear decomposition of a connected graph is a partition of the edges into a sequence of paths $L_1,...,L_r$ such that $L_1$ is a cycle and only the endpoints of $L_i$ belongs to $L_1+cdots+L_{i-1}$ for $i ge 2$. The paths $L_1,...,L_r$ are called ears. Ear decomposition has been used to characterize several important classes of graphs. We can use ear decompositions to solve a difficult problem in combinatorial commutative algebra, which investigates algebraic structures associated with combinatorial objects. The lecture will concentrate on combinatorial aspects of the solution, which should be accessible for everyone with a basic knowledge in graph theory