Periodica Mathematica Hungarica
Volume/Issue:
Volume 19: Issue 3
Variations on a theorem of Petersen
Authors: K. S. Bagga 1 , L. W. Beineke 1 , G. Chartrand 2 , and O. R. Oellermann 2
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  • 1 Department of Mathematics Indiana Purdue University 46805 Fort Wayne IN USA
  • 2 Department of Mathematics Western Michigan University 49008 Kalamazoo MI USA
DOI:
https://doi.org/10.1007/bf01850293
Page Count:
241–247
Publication Date:
01 Sep 1988
Online Publication Date:
14 Jul 2005
Article Category:
Research Article
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For an (r − 2)-edge-connected graphG (r ≥ 3) for orderp containing at mostk edge cut sets of cardinalityr − 2 and for an integerl with 0 ≤l ≤ ⌊p/2⌋, it is shown that (1) ifp is even, 0 ≤k ≤ r(l + 1) − 1, and

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathop \sum \limits_{v \in V(G)} |\deg _G v - r|< r(2 + 2l) - 2k$$ \end{document}
, then the edge independence numberβ1(G) is at least (p − 2l)/2, and (2) ifp is odd, The sharpness of these results is discussed.

Cover Periodica Mathematica Hungarica
Periodica Mathematica Hungarica
Print ISSN:
0031-5303
Online ISSN:
1588-2829
Keywords:
Primary 05C70; Secondary 05C40

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