It was conjectured by Thomassen ([B. Alspach, C. Godsil, Cycle in graphs, Ann. Discrete Math. 27 (1985)], p. 466) that every longest circuit of a 3-connected graph must have a cho...
Let G be a connected, locally connected, claw-free graph of order n and x, y be two vertices of G. In this paper, we prove that if for any 2-cut S of G, S {x, y} = , then each (x...
Abstract. We present an expected polynomial time algorithm to generate a labeled planar graph uniformly at random. To generate the planar graphs, we derive recurrence formulas that...
Let G be a simple connected graph with n vertices and n edges which we call an unicyclic graph. In this paper, we first investigate the least eigenvalue n(G), then we present two ...
The logical and algorithmic properties of stable conditional independence (CI) as an alternative structural representation of conditional independence information are investigated...