In this paper, we give graph-theoretic algorithms of linear time to the Minimum All-Ones Problem for unicyclic and bicyclic graphs. These algorithms are based on a graph-theoretic algorithm of linear time to the Minimum All-Ones Problem with Restrictions for trees.
Let G be an (edge-)colored graph. A path (cycle) is called monochromatic if all the edges of it have the same color, and is called heterochromatic if all the edges of it have different colors. In this note, some sufficient conditions for the existence of monochromatic and heterochromatic paths and cycles are obtained. We also propose a conjecture on the existence of paths and cycles with many colors.
In this paper, some new families of integral trees with diameters 4 and 6 are given. Most of these classes are infinite. They are different from those in existing literatures. The discovery of these integral trees is a new contribution to the search of such trees.
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SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.