The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Journal of Automated Reasoning - Special issue on new trends in automated reasoning
Linear ordering on graphs, anti-founded sets and polynomial time computability
Theoretical Computer Science
Set theory for computing: from decision procedures to declarative programming with sets
Set theory for computing: from decision procedures to declarative programming with sets
Minimizing the size of an identifying or locating-dominating code in a graph is NP-hard
Theoretical Computer Science
A linear algorithm for minimum 1-identifying codes in oriented trees
Discrete Applied Mathematics
Fixed-point definability and polynomial time
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Fixed-point definability and polynomial time on chordal graphs and line graphs
Fields of logic and computation
Computational Logic and Set Theory: Applying Formalized Logic to Analysis
Computational Logic and Set Theory: Applying Formalized Logic to Analysis
Reasoning, Action and Interaction in AI Theories and Systems
On a new class of codes for identifying vertices in graphs
IEEE Transactions on Information Theory
Set Graphs. III. Proof Pearl: Claw-Free Graphs Mirrored into Transitive Hereditarily Finite Sets
Journal of Automated Reasoning
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A graph G is said to be a set graph if it admits an acyclic orientation which is also extensional, in the sense that the out-neighborhoods of its vertices are pairwise distinct. Equivalently, a set graph is the underlying graph of the digraph representation of a hereditarily finite set. In this paper, we initiate the study of set graphs. On the one hand, we identify several necessary conditions that every set graph must satisfy. On the other hand, we show that set graphs form a rich class of graphs containing all connected claw-free graphs and all graphs with a Hamiltonian path. In the case of claw-free graphs, we provide a polynomial-time algorithm for finding an extensional acyclic orientation. Inspired by manipulations of hereditarily finite sets, we give simple proofs of two well-known results about claw-free graphs. We give a complete characterization of unicyclic set graphs, and point out two NP-complete problems closely related to the problem of recognizing set graphs. Finally, we argue that these three problems are solvable in linear time on graphs of bounded treewidth.