Jul 31, 2018 · A k -bisection of a bridgeless cubic graph G is a 2-colouring of its vertex set such that the colour classes have the same cardinality and ...

It is shown that every infinite locally finite bridgeless k-indivisible graph with a 2-basis admits a cycle double cover for infinite planar graphs. Expand.

Aug 31, 2012 · For ϕΓ(k), there is a simple contraction-deletion property giving us information about the polynomiality and degree of this counting function.

A k-pattern is a uniform, strong 2-cell imbedding in which every region is bounded by exactly k sides. The existence of k-patterns for all values of k > 3 and ...

Theorem K. [4] If every finite bridgeless graph has a cycle double cover, then so does every infinite locally finite bridgeless graph.

Mar 11, 2018 · A 3-regular graph with fewer than 3 bridges has a perfect matching. For any k≥3, we can construct an unmatchable cubic graph with exactly k bridges.

A \emph{$k$--bisection} of a bridgeless cubic graph $G$ is a $2$--colouring of its vertex set such that the colour classes have the same cardinality and all ...

Theorem: A graph G admits a k-NZF (for some k that might depend on G) iff it is bridgeless. Lemma: The flow along any (directed) cut is zero. Proof (of the ...

Dec 19, 2015 · For every graph G and positive integer k we have the following equiv- alence: G has a nowhere-zero k-flow if and only if G has a nowhere-zero Zk ...

Now, a graph is bridgeless if and only if it does not contain the single line. K, as a block. Thus the method of [ 171 already offers a method of counting.