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We introduce a new invariant of a cubic graph - its regular defect - which is defined as the smallest number of edges left uncovered by any collection of three perfect matchings that have no edge in common. This invariant is a modification of defect,
Externí odkaz:
http://arxiv.org/abs/2312.13638
A set of vertices of a graph $G$ is said to be decycling if its removal leaves an acyclic subgraph. The size of a smallest decycling set is the decycling number of $G$. Generally, at least $\lceil(n+2)/4\rceil$ vertices have to be removed in order to
Externí odkaz:
http://arxiv.org/abs/2309.11606
The colouring defect of a cubic graph is the smallest number of edges left uncovered by any set of three perfect matchings. While $3$-edge-colourable graphs have defect $0$, those that cannot be $3$-edge-coloured (that is, snarks) are known to have d
Externí odkaz:
http://arxiv.org/abs/2308.13639
A long-standing conjecture of Berge suggests that every bridgeless cubic graph can be expressed as a union of at most five perfect matchings. This conjecture trivially holds for $3$-edge-colourable cubic graphs, but remains widely open for graphs tha
Externí odkaz:
http://arxiv.org/abs/2210.13234
In the present paper we investigate the faithfulness of certain linear representations of groups of automorphisms of a graph $X$ in the group of symmetries of the Jacobian of $X$. As a consequence we show that if a $3$-edge-connected graph $X$ admits
Externí odkaz:
http://arxiv.org/abs/2206.01469
This paper focuses on the classification of classes of topological equivalence of finite group actions on Riemann surfaces. By the Riemann-Hurwitz bound, there are just finitely many groups that act conformally on a closed orientable surface $\mathca
Externí odkaz:
http://arxiv.org/abs/2203.05812
Autor:
Ivan Gušić, Josip Benić
Publikováno v:
Geologia Croatica, Vol 49, Iss 2, Pp 355-357 (2010)
Externí odkaz:
https://doaj.org/article/9e2b1710e545486baf8379171a153186
Publikováno v:
In Discrete Mathematics August 2024 347(8)
Publikováno v:
In Journal of Pure and Applied Algebra June 2024 228(6)