Graphs of given genus and arbitrarily large maximum genus
نویسندگان
چکیده
منابع مشابه
The maximum genus of diameter three graphs
The maximum gen'us of connected of orient able surface on which G has 2-ce11 C:U.UYC;UUULl.".. to 2,M(G) where (3(G) the Betti n'umber of G.
متن کاملThe maximum genus of vertex-transitive graphs
Graphs possessing a high degree of symmetry have often been considered in topological graph theory. For instance, a number of constructions of genus embeddings by means of current or voltage graphs is based on the observation that a graph can be represented as a Cayley graph for some group. Another kind of embedding problems where symmetrical graphs are encountered is connected with regular map...
متن کاملJoint-Tree Model and the Maximum Genus of Graphs
The vertex v of a graph G is called a 1-critical-vertex for the maximum genus of the graph, or for simplicity called 1-critical-vertex, if G − v is a connected graph and γM (G − v) = γM (G) − 1. In this paper, through the joint-tree model, we obtained some types of 1-critical-vertex, and get the upper embeddability of the Spiral S m.
متن کاملThe maximum genus of graphs of diameter two
Skoviera, M., The maximum genus of graphs of diameter two, Discrete Mathematics 87 (1991) 175-180. Let G be a (finite) graph of diameter two. We prove that if G is loopless then it is upper embeddable, i.e. the maximum genus y,&G) equals [fi(G)/Z], where /3(G) = IF(G)1 IV(G)1 + 1 is the Betti number of G. For graphs with loops we show that [p(G)/21 2s yM(G) c &G)/Z] if G is vertex 2-connected, ...
متن کاملLower bounds for the maximum genus of 4-regular graphs∗
This paper investigates the maximum genus and upper embeddability of connected 4-regular graphs. We obtain lower bounds on the maximum genus of connected 4-regular simple graphs and connected 4-regular graphs without loops in terms of the Betti number. The definition of the Betti number is referred to [Gross and Tucker, Topological Graph Theory, New York, 1987]. Furthermore, we give examples th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1973
ISSN: 0012-365X
DOI: 10.1016/0012-365x(73)90047-2