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Results tagged with graph-theory
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user 2083
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.
8
votes
1
answer
615
views
When is a triangulation of sphere two-colorable?
Let $T$ be a triangulation of sphere. We say that $T$ is $k$-colorable if the triangles of $T$ can be assigned with $k$ colors such that any two triangles with a common edge have different colors.
I a …
- 32.1k
6
votes
Accepted
A proper definition of connectivity for hypergraphs
Think of the hypergraph as a simplicial complex $\Delta$, with the facets being the hyperedges. Consider property (*) as:
1) The $i$-skeleton of $\Delta$ is full for $0\leq i\leq k-2$ and
2) $\ …
- 30.6k
8
votes
Accepted
Definition of packing property
That Def 1 and Def 2 are equivalent is a well-known Conjecture, still open as far as I know. Curiously, you can translate the whole conjecture to the language of commutative algebra, see for example p …
- 30.6k
5
votes
1
answer
631
views
Upper bounds on number of vertices of graphs whose complements has no induced cycles of cert...
Let $G$ be a finite, simple, undirected, connected graph. Suppose that $G$ has maximal degree $d$ and the complement $G^c$ has no induced cycles of lengths $i$, for $4 \leq i \leq l$. My question is: …
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