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The strong embedding conjecture states that any 2-connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2-connected graph has a circuit double cov...
A TIGHT LOWER BOUND ON THE MAXIMUM GENUS OF 3-EDGE CONNECTED LOOPLESS GRAPHS
Maximum genus 3-edge connect
2007/12/10
It is shown that the lower bound on the maximum genus of a 3-edge connected loopless graph is at least one-third of its cycle rank. Moreover, this lower bound is tight. There are infinitely such graph...