منابع مشابه
Bonds with parity constraints
Given a connected graph G = (V,E) and three even-sized subsets A1, A2, A3 of V , when does V have a partition (S1, S2) such that G[Si] is connected and |Si ∩Aj | is odd for all i = 1, 2 and j = 1, 2, 3? This problem arises in the area of integer flow theory and has theoretical interest in its own right. The special case when |A1| = |A2| = |A3| = 2 has been resolved by Chakravarti and Robertson,...
متن کاملPlane Graphs with Parity Constraints
Let S be a set of n points in general position in the plane. Together with S we are given a set of parity constraints, that is, every point of S is labeled either even or odd. A graph G on S satisfies the parity constraint of a point p ∈ S, if the parity of the degree of p in G matches its label. In this paper we study how well various classes of planar graphs can satisfy arbitrary parity const...
متن کاملConflict-Free Graph Orientations with Parity Constraints
It is known that every multigraph with an even number of edges has an even orientation (i.e., all indegrees are even). We study parity constrained graph orientations under additional constraints. We consider two types of constraints for a multigraph G = (V,E): (1) an exact conflict constraint is an edge set C ⊆ E and a vertex v ∈ V such that C should not equal the set of incoming edges at v; (2...
متن کاملEven Bonds of Prescribed Directed Parity
Given a set S of vertices in a graph, the cocycle determined by S is the set of edges joining a vertex in S to a vertex not in S. A bond is a minimal non-empty cocycle. We characterise graphs that admit an orientation under which every bond of even cardinality has a prescribed directed parity.
متن کاملExtending Sat Solver with Parity Constraints
Current methods for solving Boolean satisfiability problem (SAT) are scalable enough to solve discrete nonlinear problems involving hundreds of thousands of variables. However, modern SAT solvers scale poorly with problems involving parity constraints (linear equations modulo 2). Gaussian elimination can be used to solve a system of linear equation effectively but it cannot be applied as such w...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2012
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2011.08.005