Excluding a small minor
نویسندگان
چکیده
منابع مشابه
Excluding a small minor
There are sixteen 3-connected graphs on eleven or fewer edges. For each of these graphs H we discuss the structure of graphs that do not contain a minor isomorphic to H.
متن کاملExcluding A Grid Minor In Planar Digraphs
In [1] we introduced the notion of tree-width of directed graphs and presented a conjecture, formulated during discussions with Noga Alon and Bruce Reed, stating that a digraph of huge tree-width has a large “cylindrical grid” minor. Here we prove the conjecture for planar digraphs, but many steps of the proof work in general. This is an unedited and unpolished manuscript from October 2001. Sin...
متن کاملExcluding a Long Double Path Minor
The ``height'' of a graph G is defined to be the number of steps to construct G by two simple graph operations. Let Bn be the graph obtained from an n-edge path by doubling each edge in parallel. Then, for any minor-closed class G of graphs, the following are proved to be equivalent: (1) Some Bn is not in G; (2) There is a number h such that every graph in G has height at most h; (3) G is well-...
متن کاملCliques in Graphs Excluding a Complete Graph Minor
This paper considers the following question: What is the maximum number of k-cliques in an n-vertex graph with no Kt-minor? This question generalises the extremal function for Kt-minors, which corresponds to the k = 2 case. The exact answer is given for t 6 9 and all values of k. We also determine the maximum total number of cliques in an n-vertex graph with no Kt-minor for t 6 9. Several obser...
متن کاملCompact Routing for Graphs Excluding a Fixed Minor
This paper concerns compact routing schemes with arbitrary node names. We present a compact name-independent routing scheme for unweighted networks with n nodes excluding a fixed minor. For any fixed minor, the scheme, constructible in polynomial time, has constant stretch factor and requires routing tables with poly-logarithmic number of bits at each node. For shortest-path labeled routing sch...
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 Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.09.001