Matching extension in toroidal quadrangulations II: the 3-extendable case
نویسندگان
چکیده
A graph G containing a perfect matching is said to be m-extendable if m ≤ (|V (G)| − 2)/2 and for every matching M with |M | = m, there is a perfect matching F in G such that M ⊆ F . In a previous paper, four of the present five authors characterized those quadrangulations of the torus which are 2-extendable. In the present work a characterization of those which are 3-extendable is obtained. Since no quadrangulation of the torus can be m-extendable for any m ≥ 4, this completes the study of m-extendability for toroidal quadrangulations. Moreover, by another previous result, it follows that we have therefore characterized all 3-extendable toroidal graphs.
منابع مشابه
2-extendability of toroidal polyhexes and Klein-bottle polyhexes
A toroidal polyhex (resp. Klein-bottle polyhex) described by a string (p, q, t) arises from a p × q-parallelogram of a hexagonal lattice by a usual torus (resp. Klein bottle) boundary identification with a torsion t. A connected graph G admitting a perfect matching is kextendable if |V(G)| ≥ 2k + 2 and any k independent edges can be extended to a perfect matching of G. In this paper, we charact...
متن کاملMatching extension in quadrangulations of the torus
A graph G is said to have the property E(m,n) if, given any two disjoint matchings M and N where |M | = m and |N | = n respectively and M ∩ N = ∅, there is a perfect matching F in G such that M ⊆ F and F ∩N = ∅. This property has been previously studied for triangulations of the plane, projective plane, torus and Klein bottle. Here this study is extended to quadrangulations of the torus.
متن کاملChromatic polynomials and toroidal graphs
The chromatic polynomials of some families of quadrangulations of the torus can be found explicitly. The method, known as ‘bracelet theory’ is based on a decomposition in terms of representations of the symmetric group. The results are particularly appropriate for studying the limit curves of the chromatic roots of these families. In this paper these techniques are applied to a family of quadra...
متن کاملMatching extension in K1, r-free graphs with independent claw centers
We say that a graph G is k-extendable if every set of k independent edges of G can be extended to a perfect matching. In the paper it is proved that if G is an even (2k + 1)-connected K 1;k+3-free graph such that the set of all centers of claws is independent, then G is k-extendable. As a corollary we obtain an analogous result for almost claw-free graphs and for claw-free graphs, thus extendin...
متن کاملA recursive theorem on matching extension
A graph G having a perfect matching (or I-factor) is called n-fextendable if every matching of size n is extended to a I-factor. Further, G is said to be (r : m, n }-extendable if, for every connected subgraph S of order 2r for which G \ V(S) is connected, S is m-extendable and G \ V(S) is nextendable. We prove the following: Let p, r, m, and n be positive integers with p r > nand r > m. Then e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Australasian J. Combinatorics
دوره 63 شماره
صفحات -
تاریخ انتشار 2015