Isomorphism of graphs of bounded valence can be tested in polynomial time

The Structure of Level-k Phylogenetic Networks

“…The algorithm, BuildGenerators, detailed below, works by simply trying to apply rules R1 and R2 on any generator in S * k , then removing the isomorphic ones. To prove the polynomial complexity, the main point is the fact that the isomorphism test which is Graph Isomorphismcomplete on general digraphs [35], can be done, in our case, in polynomial time [25,27] in the size of the graph which is polynomial in |S * k | by propositions 2.3 and 2.4. The proof is also detailed in Appendix D.…”

“…However, here we restrict to instances where the digraphs have maximal degree 3 in particular, and isomorphism for graphs of bounded maximum degree can be determined in polynomial time [25]. We now show how to polynomially reduce the problem of isomorphism for digraphs of maximum degree 3 and maximum outdegree and indegree 2 to the problem of isomorphism for graphs of bounded degree.…”

Some Algorithmic Problems in Polytope Theory

“…In constant dimension the problem can be solved in polynomial time by a reduction [34] to the graph isomorphism problem for graphs of bounded degree, for which a polynomial time algorithm is known (Luks [41]). Problem 21 can polynomially be reduced to this problem.…”

Efficient subgraph matching using topological node feature constraints

“…This idea was extended by Sorlin and Solnon to create the IDL algorithm [14]. Some polynomial-time algorithms have been developed for special cases of graph isomorphism, such as planar graphs [15] and bounded valence graphs [16]. A recent paper by Fankhauser et al [17] presents a polynomialtime algorithm for graph isomorphism in the general case.…”