Data structures and network algorithms
Data structures and network algorithms
Compatible path-cycle-decompositions of plane graphs
Journal of Combinatorial Theory Series B
On circuit decomposition of planar eulerian graphs
Journal of Combinatorial Theory Series B
Discrete Applied Mathematics
Alternating cycles and trails in 2-edge-coloured complete multigraphs
Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
Paths and trails in edge-colored graphs
Theoretical Computer Science
Properly Coloured Cycles and Paths: Results and Open Problems
Graph Theory, Computational Intelligence and Thought
Paths and trails in edge-colored graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Complexity of paths, trails and circuits in arc-colored digraphs
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Complexity of trails, paths and circuits in arc-colored digraphs
Discrete Applied Mathematics
| Hi-index | 0.05 |
Let v be a vertex of a graph G; a transition graph T(v) of v is a graph whose vertices are the edges incident with v. We consider graphs G with prescribed transition systems T = {T(v)|v ∈ V(G)}. A path P in G is called T-compatible, if each pair uv, vw of consecutive edges of P form an edge in T(v). Let A be a given class of graphs (closed under isomorphism). We study the computational complexity of finding T-compatible paths between two given vertices of a graph for a specified transition system T ⊆ A. Our main result is that a dichotomy holds (subject to the assumption P ≠ NP). That is, for a considered class A, the problem is either (1) NP-complete, or (2) it can be solved in linear time. We give a criterion--based on vertex induced subgraphs--which decides whether (1) or (2) holds for any given class A.