منابع مشابه
Labeled K2, t Minors in Plane Graphs
Let G be a 3-connected planar graph and let U ⊆ V (G). It is shown that G contains a K2,t minor such that t is large and each vertex of degree 2 in K2,t corresponds to some vertex of U if and only if there is no small face cover of U . This result cannot be extended to 2-connected planar graphs.
متن کاملThe edge-density for K2, t minors
Let H be a graph. If G is an n-vertex simple graph that does not contain H as a minor, what is the maximum number of edges that G can have? This is at most linear in n, but the exact expression is known only for very few graphs H . For instance, when H is a complete graph Kt, the “natural” conjecture, (t− 2)n− 12(t− 1)(t− 2), is true only for t ≤ 7 and wildly false for large t, and this has rat...
متن کاملKt Minors in Large t-Connected Graphs
It appears that for t ≥ 6 the structure of large (t− 1)-connected graphs with no Kt minor is prohibitively complicated. Moreover, for t ≥ 8 the assumption in the above conjecture that |V (G)| is large is also necessary. In fact, Thomason has shown that there exist Θ(t √ log t)-connected graphs with no Kt-minor, but all known examples are bounded in size by a function of t. Thus, the conditions ...
متن کاملKs, t Minors in (s+t)- Chromatic Graphs, II
Let K∗ s,t denote the graph obtained from the complete graph Ks+t by deleting the edges of some Kt-subgraph. The author proved earlier that for each fixed s and t > t0(s) := max{415s 2+s, (240s log2 s)8s log2 s+1}, every graph with chromatic number s + t has a K∗ s,t minor. This confirmed a partial case of the corresponding conjecture by Woodall and Seymour. In this paper we show that the state...
متن کاملOn Ks, t minors in (s+t)-chromatic graphs
Let K∗ s,t denote the graph obtained from the complete graph Ks+t by deleting the edges of some Kt -subgraph. We prove that for each fixed s and sufficiently large t, every graph with chromatic number s+t has a K∗ s,t minor. 2010 Wiley Periodicals, Inc. J Graph Theory 65: 343–350, 2010 MSC 2000: 05 C 15; 05 C 83
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2002
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2083