Distance-Restricted Matching Extension in Triangulations of the Torus and the Klein Bottle
نویسندگان
چکیده
منابع مشابه
Distance-Restricted Matching Extension in Triangulations of the Torus and the Klein Bottle
A graph G with at least 2m + 2 edges is said to be distance d m-extendable if for any matching M in G with m edges in which the edges lie pair-wise distance at least d, there exists a perfect matching in G containing M . In a previous paper, Aldred and Plummer proved that every 5-connected triangulation of the plane or the projective plane of even order is distance 5 m-extendable for any m. In ...
متن کاملDistance-Restricted Matching Extension in Triangulations on the Torus and the Klein Bottle
A graph G with at least 2m+2 edges is said to be distance d m-extendable if for any matching M of G with m edges in which the edges lie pair-wise distance at least d, there exists a perfect matching of G containing M . In [J. Graph Theory 67 (2011), no. 1, 38-46], Aldred and Plummer proved that every 5-connected triangulation on the plane or the projective plane with an even order is distance 5...
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Aldred and Plummer proved that every 6-connected even graph minimally embedded on the torus or the Klein bottle is E(1, n)(n ≤ 3) and E(0, n)(n ≤ 5) [R.E.L. Aldred, M.D. Plummer, Restricted matching in graphs of small genus, Discrete Math. 308 (2008) 5907–5921]. In this paper, we can remove the upper bounds on n by showing that every even 6-regular graph G embedded on the torus or the Klein bot...
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A combinatorial 2-manifold is called weakly regular if the action of its automorphism group on its vertices is transitive. A combinatorial 2-manifold is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular combinatorial 2-manifold is degree-regular. In [5], Lutz has classified all the weakly-regular combinatorial 2-manifolds on at most 15 vertices, among...
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We show that an Eulerian triangulation of the Klein bottle has chromatic number equal to six if and only if it contains a complete graph of order six, and it is 5-colorable, otherwise. As a consequence of our proof, we derive that every Eulerian triangulation of the Klein bottle with facewidth at least four is 5-colorable.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/2952