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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 a Geoff WHITTLE. Bridging Separations in Matroids. \textit{SIAM Journal on Discrete Mathematics}. Philadelphia: SIAM, 2005, roč.~18, č.~3, s.~638-646. ISSN~0895-4801.
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