Eulerian cycle in a grid graph
Source: 2022 China TST, Test 2, P1
March 28, 2022
graph theorygridcombinatorics
Problem Statement
Find all pairs of positive integers , such that in a table (with horizontal lines and vertical lines), a diagonal can be drawn in some unit squares (some unit squares may have no diagonals drawn, but two diagonals cannot be both drawn in a unit square), so that the obtained graph has an Eulerian cycle.