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Full-Text Articles in Mathematics
Decisive Neutrality, Restricted Decisive Neutrality, And Split Decisive Neutrality On Median Semilattices And Median Graphs., Ulf Högnäs
Electronic Theses and Dissertations
Consensus functions on finite median semilattices and finite median graphs are studied from an axiomatic point of view. We start with a new axiomatic characterization of majority rule on a large class of median semilattices we call sufficient. A key axiom in this result is the restricted decisive neutrality condition. This condition is a restricted version of the more well-known axiom of decisive neutrality given in [4]. Our theorem is an extension of the main result given in [7]. Another main result is a complete characterization of the class of consensus on a finite median semilattice that satisfies the axioms …
Partially Oriented 6-Star Decomposition Of Some Complete Mixed Graphs, Kazeem A. Kosebinu
Partially Oriented 6-Star Decomposition Of Some Complete Mixed Graphs, Kazeem A. Kosebinu
Electronic Theses and Dissertations
Let $M_v$ denotes a complete mixed graph on $v$ vertices, and let $S_6^i$ denotes the partial orientation of the 6-star with twice as many arcs as edges. In this work, we state and prove the necessary and sufficient conditions for the existence of $\lambda$-fold decomposition of a complete mixed graph into $S_6^i$ for $i\in\{1,2,3,4\}$. We used the difference method for our proof in some cases. We also give some general sufficient conditions for the existence of $S_6^i$-decomposition of the complete bipartite mixed graph for $i\in\{1,2,3,4\}$. Finally, this work introduces the decomposition of a complete mixed graph with a hole into …