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Splitter Theorems for Cubic Graphs

Published online by Cambridge University Press:  07 April 2006

GUOLI DING  and
JINKO KANNO
GUOLI DING
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803, USA (e-mail: ding@math.lsu.edu)
JINKO KANNO
Affiliation:
Mathematics and Statistics Program, Louisiana Tech University, Ruston, Louisiana 71272, USA (e-mail: jkanno@latech.edu)
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Abstract

Let $\Gamma_{k,g}$ be the class of $k$-connected cubic graphs of girth at least $g$. For several choices of $k$ and $g$, we determine a set ${\cal O}_{k,g}$ of graph operations, for which, if $G$ and $H$ are graphs in $\Gamma_{k,g}$, $G\not\cong H$, and $G$ contains $H$ topologically, then some operation in ${\cal O}_{k,g}$ can be applied to $G$ to result in a smaller graph $G'$ in $\Gamma_{k,g}$ such that, on one hand, $G'$ is contained in $G$ topologically, and on the other hand, $G'$ contains $H$ topologically.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 15 , Issue 3 , May 2006 , pp. 355 - 375
Copyright
2006 Cambridge University Press

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