Let G be a graph without even cycles or isolated vertices. Prove that every block of G

is an edge or an odd cycle.

Can someone show this proof? Thanks so much!!

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- October 25th 2010, 10:31 PMjzelltEven Cycles
Let G be a graph without even cycles or isolated vertices. Prove that every block of G

is an edge or an odd cycle.

Can someone show this proof? Thanks so much!! - October 27th 2010, 12:06 PMtom@ballooncalculus
A block that isn't an edge can't have any vertices of degree one. So it must be the sum of one or more cycle graphs. And these have to be odd. Two cycle graphs must have at least two vertices in common for their sum to be a block (why?). And summing two distinct odd cycle graphs that do share at least two vertices creates ... which glitch?