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math.CO2021
Erdős-Gyárfás Conjecture for -free graphs
Yuping Gao, Songling Shan
A graph is -free if it contains no induced subgraph isomorphic to the path on eight vertices. In 1995, Erdős and Gyárfás conjectured that every graph of minimum degree a…
math.CO2021
Hamiltonian cycles in 7-tough -free graphs
Yuping Gao, Songling Shan
The toughness of a noncomplete graph is the maximum real number such that the ratio of to the number of components of is at least for every cutset of $G…