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Variations on a theorem of Petersen. (English) Zbl 0695.05035

Authors’ abstract: “For an \((r-2)\)-edge-connected graph G \((r\geq 3)\) [of] order p containing at most k edge cut sets of cardinality \(r-2\) and for an integer \(\ell\) with \(0\leq \ell \leq \lfloor p/2\rfloor\), it is shown that (1) if p is even, \(0\leq k\leq r(\ell +1)-1\), and \(\sum_{v\in V(G)}| \deg_ Gv-r| <r(2+2\ell)-2k,\) then the edge independence number \(\beta_ 1(G)\) is at least (p-2\(\ell)/2\), and (2) if p is odd, \(0\leq k\leq [r(3+2\ell)-1]/2,\) and \(\sum_{v\in V(G)}| \deg_ Gv- r| <r(3+2\ell)-2k,\) then \(\beta_ 1(G)\geq (p-2\ell -1)/2.\) The sharpness of these results is discussed.”
Reviewer: R.C.Entringer

MSC:

05C40 Connectivity
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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References:

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