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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.
1
vote
Accepted
Decomposition of a regular graph and connected subgraphs
Edit: How about this counterexample for the case $s_2,t_2>0$:
$G=(V,E)$ with $V=\{x_1\}\cup\{u_i^k\ |\ 1\le i\le n,1\le k\le 4\}$, and $E$ being the union of
$\{(x_1,u_i^k)\ |\ 1\le i\le n, k\in\{1 …
4
votes
Find all faces in a graph from list of edges
Expanding a bit on the comments to Federico's answer: If the neighbors of each vertex are listed in counterclockwise order, this defines an embedding on a surface, and if this information was obtained …