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@article{575450,
author = {Hliněný, Petr and Geelen, Jim and Whittle, Geoff},
article_location = {Philadelphia},
article_number = {3},
keywords = {matroid; separation},
language = {eng},
issn = {0895-4801},
journal = {SIAM Journal on Discrete Mathematics},
title = {Bridging Separations in Matroids},
volume = {18},
year = {2005}
}
TY - JOUR
ID - 575450
AU - Hliněný, Petr - Geelen, Jim - Whittle, Geoff
PY - 2005
TI - Bridging Separations in Matroids
JF - SIAM Journal on Discrete Mathematics
VL - 18
IS - 3
SP - 638
EP - 638
PB - SIAM
SN - 08954801
KW - matroid
KW - separation
N2 - Let $(X_1,X_2)$ be an exact $k$--separation of a matroid $N$. If $M$ is a matroid that contains $N$ as a minor and the $k$--separation $(X_1,X_2)$ does not extend to a $k$--separation in $M$ then we say that $M$ {\em bridges} the $k$--separation $(X_1,X_2)$ in $N$. One would hope that a minor minimal bridge for $(X_1,X_2)$ would not be much larger than $N$. Unfortunately there are instances in which one can construct arbitaraily large minor minimal bridges. We restrict our attention to the class of matroids representable over a fixed finite field and show that here minor minimal bridges are bounded in size.
ER -
HLINĚNÝ, Petr, Jim GEELEN and Geoff WHITTLE. Bridging Separations in Matroids. \textit{SIAM Journal on Discrete Mathematics}. Philadelphia: SIAM, 2005, vol.~18, No~3, p.~638-646. ISSN~0895-4801.
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