An Erdos-Gallai Theorem for Matroids

被引：1

作者：

McGuinness, Sean ^{[1
]}

机构：

[1] Thompson Rivers Univ, Dept Math, Kamloops, BC V2C 5N3, Canada

来源：

ANNALS OF COMBINATORICS | 2012年 / 16卷 / 01期

关键词：

matroid; binary matroid; minor;

D O I：

10.1007/s00026-011-0123-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Erdos and Gallai showed that for any simple graph with n vertices and circumference c it holds that |E(G)| <= 1/2 (n-1)c. We extend this theorem to simple binary matroids having no F-7-minor by showing that for such a matroid M with circumference c(M) >= 3 it holds that E(G)| <= 1/2 r(M)c(M).

引用

页码：107 / 119

页数：13

共 50 条

[41] ON A THEOREM OF ERDOS AND SZEKERES
SUBBARAO, MV
[J]. CANADIAN MATHEMATICAL BULLETIN, 1968, 11 (04): : 597 - &
[42] ON A THEOREM OF ERDOS AND TURAN
ENNOLA, V
[J]. MATHEMATICA SCANDINAVICA, 1968, 22 (01) : 75 - &
[43] VARIATIONS ON THE GALLAI-MILGRAM THEOREM
HARTMAN, IB
[J]. DISCRETE MATHEMATICS, 1988, 71 (02) : 95 - 105
[44] MENGERS THEOREM AND MATROIDS
BRUALDI, RA
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1971, 4 (JUL): : 46 - &
[45] A chain theorem for matroids
Oxley, James
Semple, Charles
Whittle, Geoff
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2008, 98 (03) : 447 - 483
[46] MENGERS THEOREM FOR MATROIDS
TUTTE, WT
[J]. JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS SECTION B-MATHEMATICS AND MATHEMATICAL, 1965, B 69 (1-2): : 49 - +
[47] Sylvester–Gallai Theorem and Metric Betweenness
Vasek Chvátal
[J]. Discrete & Computational Geometry, 2004, 31 : 175 - 195
[48] A constructive version of the Sylvester–Gallai theorem
M. Mandelkern
[J]. Acta Mathematica Hungarica, 2016, 150 : 121 - 130
[49] A generalization of the Gallai-Roy theorem
Li, H
[J]. GRAPHS AND COMBINATORICS, 2001, 17 (04) : 681 - 685
[50] On the Sylvester-Gallai theorem for conics
Czaplinski, A.
Dumnicki, M.
Farnik, L.
Gwozdziewicz, J.
Lampa-Baczynska, M.
Malara, Grzegorz
Szemberg, T.
Szpond, J.
Tutaj-Gasinska, H.
[J]. RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, 2016, 136 : 191 - 203

← 1 2 3 4 5 →