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Slilaty, Daniel. (1403). Graphs without a $2C_3$-minor and bicircular matroids without a $U_{3,6}$-minor. , 13(2), 165-167. doi: 10.22108/toc.2023.134261.1998
Daniel Slilaty. "Graphs without a $2C_3$-minor and bicircular matroids without a $U_{3,6}$-minor". , 13, 2, 1403, 165-167. doi: 10.22108/toc.2023.134261.1998
Slilaty, Daniel. (1403). 'Graphs without a $2C_3$-minor and bicircular matroids without a $U_{3,6}$-minor', , 13(2), pp. 165-167. doi: 10.22108/toc.2023.134261.1998
Slilaty, Daniel. Graphs without a $2C_3$-minor and bicircular matroids without a $U_{3,6}$-minor. , 1403; 13(2): 165-167. doi: 10.22108/toc.2023.134261.1998

Graphs without a $2C_3$-minor and bicircular matroids without a $U_{3,6}$-minor

Transactions on Combinatorics
مقاله 6، دوره 13، شماره 2، شهریور 2024، صفحه 165-167    اصل مقاله (364.84 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2023.134261.1998
نویسنده
Daniel Slilaty*
Department of Mathematics and Statistics, Wright State University Dayton, OH 45435, USA
چکیده
In this note we characterize all graphs without a $2C_3$-minor. A consequence of this result is a characterization of the bicircular matroids with no $U_{3,6}$-minor.
کلیدواژه‌ها
$2C_3$-minor؛ $U_{3؛ 6}$-minor؛ bicircular matroid
مراجع

[1] C. R. Coullard, J. G. del Greco and D. K. Wagner, Representations of bicircular matroids, Discrete Appl. Math.,
32 (1991) 223–240.
[2] R. Diestel, Simplicial decompositions of graphs: a survey of applications, Graph theory and combinatorics (Cam-
bridge, 1988). Discrete Math., 75 (1989) 121–144.
[3] G. Ding and C. Liu, Excluding a small minor, Discrete Appl. Math., 161 (2013) 355–368.
[4] D. W. Hall, A note on primitive skew curves, Bull. Amer. Math. Soc., 49 (1943) 935–936.
[5] J. Oxley, Matroid theory, second ed., Oxford Graduate Texts in Mathematics, 21, Oxford University Press, Oxford,
2011.
[6] W. T. Tutte, Connectivity in matroids, Canadian J. Math., 18 (1966) 1301–1324.
[7] K. Wagner, Über eine Eigenschaft der ebenen Komplexe, Math. Ann., 114 (1937) 570–590.
[8] T. Zaslavsky, Biased graphs. II. The three matroids, J. Combin. Theory Ser. B, 51 (1991) 46–72.

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