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math.CO2019★ 2 cited
Nonempty intersection of longest paths in graphs without forbidden pairs
Yuping Gao, Songling Shan
In 1966, Gallai asked whether all longest paths in a connected graph have a nonempty intersection. The answer to this question is not true in general and various counterexamples ha…
math.CO2019★ 1 cited
Equitable partition of plane graphs with independent crossings into induced forests
Bei Niu, Xin Zhang, Yuping Gao
The cluster of a crossing in a graph drawing in the plane is the set of the four end-vertices of its two crossed edges. Two crossings are independent if their clusters do not inter…