We want to derive a linear in (n−k) bound on the number of edges in a graph that does not contain (k+1)-connected subgraphs. But the bound becomes linear only for graphs with large number of vertices; while for small graphs the dependency is quadratic in n−k. The main difficult...
He also conjectured that for $n$ large with respect to $k$, every such graph has at most $\\\frac{3}{2}\\\left(k - \\\frac{1}{3}ight)(n-k)$ edges. Yuster improved Mader's upper bound to $\\\frac{193}{120}(n-k)$ for $n\\\geq\\\frac{9k}{4}$. In this note...
A LOWER BOUND FOR THE NUMBER OFEDGES IN A GRAPH CONTAINING NO TWOCYCLES OF THE SAME LENGTHChunhui Lai∗Dept. of Math., Zhangzhou Teachers College,Zhangzhou, Fujian 363000, P. R. of CHINA.zjlaichu@public. zzptt. fj. cnSubmitted: November 3, 2000; Accepted: October 20, 2001.MR ...
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2.1.134 Part 1 Section 17.4.21, hideMark (Ignore End Of Cell Marker In Row Height Calculation) 2.1.135 Part 1 Section 17.4.22, insideH (Table Inside Horizontal Edges Border) 2.1.136 Part 1 Section 17.4.23, insideH (Table Cell Inside Horizontal Edges Border) 2.1.137 Part ...
All graphs in this paper are finite and simple. A subdivision of a graph G is a graph obtained from G by replacing the edges of G with independent paths of length at least one between their end vertices. For a positive integer n, we use Kn to denote a complete graph on n vertices....
[ +1 ms] at org.gradle.internal.graph.CachingDirectedGraphWalker$GraphWithEmptyEdges.getNodeValues(CachingDirectedGraphWalker.java:213) [ +1 ms] at org.gradle.internal.graph.CachingDirectedGraphWalker.doSearch(CachingDirectedGraphWalker.java:121) [ ] at org.gradle.internal.graph.CachingDirectedGraphWalk...
A geometric graph is a graph G = (V, E) drawn in the plane so that the vertex set V consists of points in general position and the edge set E consists of straight line segments between points of V. It is known that, for any fixed k, any geometric graph G
A graph is a mathematical structure consisting of vertices, edges, and a set of non-empty sets called circuits. A graph is connected if at least one path exists between every pair of vertices. A nontrivial circuit is a subset of vertices with no edges in common....
It is known that, for any fixed k , any geometric graph G on n vertices with no k pairwise crossing edges contains at most O ( n log n ) edges. In this paper we give a new, simpler proof of this bound, and show that the same bound holds also when the edges of G are ...