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Full-Text Articles in Physical Sciences and Mathematics
On Colorings And Orientations Of Signed Graphs, Daniel Slilaty
On Colorings And Orientations Of Signed Graphs, Daniel Slilaty
Mathematics and Statistics Faculty Publications
A classical theorem independently due to Gallai and Roy states that a graph G has a proper k-coloring if and only if G has an orientation without coherent paths of length k. An analogue of this result for signed graphs is proved in this article.
Graphs Without A 2c3-Minor And Bicircular Matroids Without A U3,6-Minor, Daniel Slilaty
Graphs Without A 2c3-Minor And Bicircular Matroids Without A U3,6-Minor, Daniel Slilaty
Mathematics and Statistics Faculty Publications
In this note we characterize all graphs without a 2C3-minor. A consequence of this result is a characterization of the bicircular matroids with no U3,6-minor.
Odd Solutions To Systems Of Inequalities Coming From Regular Chain Groups, Daniel Slilaty
Odd Solutions To Systems Of Inequalities Coming From Regular Chain Groups, Daniel Slilaty
Mathematics and Statistics Faculty Publications
Hoffman’s theorem on feasible circulations and Ghouila-Houry’s theorem on feasible tensions are classical results of graph theory. Camion generalized these results to systems of inequalities over regular chain groups. An analogue of Camion’s result is proved in which solutions can be forced to be odd valued. The obtained result also generalizes the results of Pretzel and Youngs as well as Slilaty. It is also shown how Ghouila-Houry’s result can be used to give a new proof of the graph- coloring theorem of Minty and Vitaver.