تعداد نشریات | 43 |
تعداد شمارهها | 1,655 |
تعداد مقالات | 13,542 |
تعداد مشاهده مقاله | 31,062,084 |
تعداد دریافت فایل اصل مقاله | 12,221,253 |
A new proof of validity of Bouchet's conjecture on Eulerian bidirected graphs | ||
Transactions on Combinatorics | ||
مقاله 8، دوره 6، شماره 2، شهریور 2017، صفحه 31-35 اصل مقاله (230.11 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2017.21362 | ||
نویسنده | ||
Narges Ghareghani* | ||
University of Tehran | ||
چکیده | ||
Recently, E. Máčajová and M. Škoviera proved that every bidirected Eulerian graph which admits a nowhere zero flow, admits a nowhere zero $4$-flow. This result shows the validity of Bouchet's nowhere zero conjecture for Eulerian bidirected graphs. In this paper we prove the same theorem in a different terminology and with a short and simple proof. More precisely, we prove that every Eulerian undirected graph which admits a zero-sum flow, admits a zero-sum $4$-flow. As a conclusion we obtain a shorter proof for the previously mentioned result of Máčajová and M. Škoviera. | ||
کلیدواژهها | ||
Nowhere zero flow in bidirected graphs؛ zero-sum flow؛ Eulerian graphs | ||
مراجع | ||
[1] S. Akbari, A. Daemi, O. Hatami, A. Javanmard and A. Mehrabian, Zero-sum ows in regular graphs, Graphs Combin., 26 (2010) 603-615. [2] S. Akbari, N. Ghareghani, G. B. Khosrovshahi and A. Mahmo o di, On Zero-Sum 6-ows of Graphs, Linear Algeb. Appl., 430 (2009) 3047-3052.
[3] A. Bouchet, Nowhere-zero integral ows on a bidirected graph, J. Combin. Theory Ser. B., 34 (1983) 279-292.
[4] M. DeVos, Flows in bidirected graphs, arXiv:1310.8406.
[5] P. Hell and X. Zhu, On the Adaptable Chromatic Numb er of Graphs, European J. Combin., 29 (2008) 912-921.
[6] E. Maca jova and M. Skoviera, Nowhere-zero ows on signed Eulerian graphs, arXiv:1408.1703.
[7] D. B. West, Introduction to Graph Theory, Prentice Hall, Inc., Upp er Saddle River, 2001.
[8] O. Zyka, Nowhere-Zero 30 -Flow on Bidirected Graphs, Thesis, Charles University, Praha, 1987. | ||
آمار تعداد مشاهده مقاله: 708 تعداد دریافت فایل اصل مقاله: 536 |