We estimate the minimum number of vertices of a cubic graph with given oddness and cyclic connectivity. We prove that a bridgeless cubic graph G with oddness Ï‰(G) other than the Petersen graph has atâ€¦ (More)

A graph G is k-degenerate if it can be transformed into an empty graph by subsequent removals of vertices of degree k or less. We prove that every connected planar graph with average degree d > 2 hasâ€¦ (More)

Finally, for a cyclically 7-edge connected snark G we prove the following weakening of Jaeger-Swart conjecture. We prove that given one vertex v of G, we can choose F so that v is not in a 7-circuitâ€¦ (More)

We show that every bridgeless cubic graph G on n vertices other than the Petersen graph has a 2-factor with at most 2(nâˆ’2)/15 circuits of length 5. An infinite family of graphs attains this bound. Weâ€¦ (More)

Let tsp(G) denote the length of a shortest travelling salesman tour in a graph G. We prove that for any Îµ > 0, there exists a simple 2-connected planar cubic graph G1 such that tsp(G1) â‰¥ (1.25 âˆ’ Îµ) Â·â€¦ (More)