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Results tagged with graph-theory
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user 50335
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
2
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59
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Maximum number of edges on $2^{k-1}+s$ vertices of a $k$-dimensional cube?
Let $k$ be an even number. For a $k$-dimensional cube (http://mathworld.wolfram.com/HypercubeGraph.html) $Q_k$, let $G$ be a subgraph of $Q_k$ with $2^{k-1}+s$ vertices, for $1\le s\le 2^{k-1}-1$. I a …
- 281
1
vote
2
answers
351
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Tight bound of Turan number for K_{1,t,t}
I'm looking for a tight bound for Turan number $ex_2(n,K_{1,t,t})$, where $K_{1,t,t}$ is the complete 3-partite graph with parts of size 1, t, and t.
The motivation is that we now $ex_2(n,K_{t,t})=O( …
- 281
1
vote
1
answer
66
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Existence of dense graph with relatively small codegree?
Let $n$ be some parameter tending to infinity. I am wondering does there exists some kind of graphs $G$ on vertex-set $[n]$ with maximum degree less than $D$, so that
$D\ge n/w_1(n)$,
$e_G$, the nu …
- 281
1
vote
1
answer
128
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Find large "induced" bipartite graph in a dense graph?
Do there exist constants $d>0$, $0<c<1$, $\delta>0$ so that for all large $n$, there exists a graph $H$ satisfying $$e_H\ge dn^2,$$ and then no matter how we remove some edges from $H$ to get an $n$-v …
- 281
0
votes
1
answer
415
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Reference for Turan Density
I am working a 3-graph problem. I convert it to calculate Turan density, that is $lim_{n\to \infty}\frac{ex_3(n,F)}{\binom{n}{3}}$, where F is a3-graph. I'd like to know are there some methods and cla …
- 281
0
votes
1
answer
114
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Any results concerning the numbers of vertices and edges to form fixed number of cliques in ...
Given a complete graph $K_n$, and if we know there are $t$ $K_s$ ($s\ge 2$) in it, what can we say about the possible number $a$ of vertices and the number $b$ edges to form these $t$ cliques? We can …
- 281
0
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0
answers
4
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Construct a maximum matching from a minimum vertex cover in bipartite graph?
Konig's theorem in graph theory says that for a bipartite graph $G$, the size of maximum matching in $G$ is equal to the size of minimum vertex cover of $G$.
Typically, one of the proofs is to constru …
- 281
0
votes
0
answers
7
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separator and vertex-connectivity
A definition of "separator" is the following: Let $G$ is an $n$-vertex graph, then $S\subseteq V(G)$ is a separator if there is a partition $V=A\cup B\cup S$ such that $|A|,|B|\le 2n/3$ and there is n …
- 281