3
votes
0answers
38 views

Balancing out edge multiplicites in a graph

Let $G$ be a multigraph with maximum edge multiplicity $t$ and minimum edge multiplicity $1$ (so that there is at least one 'ordinary' edge). Is there some simple graph $H$ such that the $t$-fold ...
3
votes
2answers
154 views

Is the domination number of a combinatorial design determined by the design parameters?

Let $D$ be a $(v,k,\lambda)$-design. By the domination number of $D$ I mean the domination number $\gamma(L(D))$ of the bipartite incidence graph of $D$. Is $\gamma(L(D))$ determined only by ...
6
votes
3answers
580 views

Meeting management

A friend wants to have ten meetings of six people every day for five days with no pair of people meeting twice. Is this possible? It appears to be a question about maximal decomposition of a complete ...
19
votes
2answers
2k views

Is there a 7-regular graph on 50 vertices with girth 5? What about 57-regular on 3250 vertices?

The following problem is homework of a sort -- but homework I can't do! The following problem is in Problem 1.F in Van Lint and Wilson: Let $G$ be a graph where every vertex has degree $d$. ...
23
votes
15answers
6k views

Linear Algebra Proofs in Combinatorics?

Simple linear algebra methods are a surprisingly powerful tool to prove combinatorial results. Some examples of combinatorial theorems with linear algebra proofs are the (weak) perfect graph theorem, ...