Hall-Type Results for 3-Connected Projective Graphs
نویسندگان
چکیده
4 Projective planar graphs can be characterized by a set A of 35 excluded minors. However, 5 these 35 are not equally important. A set E of 3-connected members of A is excludable if there 6 are only finitely many 3-connected non-projective planar graphs that do not contain any graph 7 in E as a minor. In this paper we show that there are precisely two minimal excludable sets, 8 which have sizes 19 and 20, respectively. 9
منابع مشابه
Nordhaus-Gaddum type results for the Harary index of graphs
The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ ...
متن کاملProjective-Planar Graphs with No K3, 4-Minor
There are several graphs H for which the precise structure of graphs that do not contain a minor isomorphic to H is known. In particular, such structure theorems are known for K5 [13], V8 [8] and [7], the cube [3], the octahedron [4], and several others. Such characterizations can often be very useful, e.g., Hadwiger’s conjecture for k = 4 is verified by using the structure for K5-free graphs, ...
متن کاملLight subgraphs of graphs embedded in the plane and in the projective plane – a survey –
It is well known that every planar graph contains a vertex of degree at most 5. A theorem of Kotzig states that every 3-connected planar graph contains an edge whose endvertices have degree-sum at most 13. Recently, Fabrici and Jendrol’ proved that every 3-connected planar graph G that contains a k-vertex path, a path on k vertices, contains also a k-vertex path P such that every vertex of P ha...
متن کاملInternally 4-connected projective-planar graphs
5 Archdeacon proved that projective-planar graphs are characterized by 35 excluded minors. 6 Using this result we show that internally 4-connected projective-planar graphs are characterized 7 by 23 internally 4-connected excluded minors. 8
متن کاملDecomposing plane cubic graphs
It was conjectured by Hoffmann-Ostenhof that the edge set of every cubic graph can be decomposed into a spanning tree, a matching and a family of cycles. We prove the conjecture for 3-connected cubic plane graphs and 3-connected cubic graphs on the projective plane. Our proof provides a polynomial time algorithm to find the decomposition for 3-connected cubic plane graphs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 82 شماره
صفحات -
تاریخ انتشار 2016