- Tytuł:
- Cores, Joins and the Fano-Flow Conjectures
- Autorzy:
-
Jin, Ligang
Steffen, Eckhard
Mazzuoccolo, Giuseppe - Powiązania:
- https://bibliotekanauki.pl/articles/31342432.pdf
- Data publikacji:
- 2018-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
cubic graphs
Fan-Raspaud Conjecture
cores
weak-cores - Opis:
- The Fan-Raspaud Conjecture states that every bridgeless cubic graph has three 1-factors with empty intersection. A weaker one than this conjecture is that every bridgeless cubic graph has two 1-factors and one join with empty intersection. Both of these two conjectures can be related to conjectures on Fano-flows. In this paper, we show that these two conjectures are equivalent to some statements on cores and weak cores of a bridgeless cubic graph. In particular, we prove that the Fan-Raspaud Conjecture is equivalent to a conjecture proposed in [E. Steffen, 1-factor and cycle covers of cubic graphs, J. Graph Theory 78 (2015) 195–206]. Furthermore, we disprove a conjecture proposed in [G. Mazzuoccolo, New conjectures on perfect matchings in cubic graphs, Electron. Notes Discrete Math. 40 (2013) 235–238] and we propose a new version of it under a stronger connectivity assumption. The weak oddness of a cubic graph G is the minimum number of odd components (i.e., with an odd number of vertices) in the complement of a join of G. We obtain an upper bound of weak oddness in terms of weak cores, and thus an upper bound of oddness in terms of cores as a by-product.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2018, 38, 1; 165-175
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł