Tough graphs and hamiltonian circuits

V. Chvátal
1973 Discrete Mathematics  
The toughness of a graph G is defined as the largest real number: t such that deletion of any s points from 6 results in a graph which is either connected or elst: has at most s/t components. Clearly, every hamiltonian graph is l-tough. Conversely, we conjecture that for some to, ewry to-tough graph is hamiltonian. Since a square of a k-connectc;d graph is always ktough., a proof of this conjecture with to = 2 would imply Fleischner's thec,rem (the square of a block is hamiltonian). We
more » ... zn infinite family of (3/2)-tough nonhamiltonian graphs. * Original version received 20 Decembeq l971; i&vised version received 29 June 1972.
doi:10.1016/0012-365x(73)90138-6 fatcat:vexd4udggbgrpfs4q5vfvf5uvm