22
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Erd\H{o}s-Gallai-type results for total monochromatic connection of graphs

      Preprint
      , ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          A graph is said to be {\it total-colored} if all the edges and the vertices of the graph are colored. A total-coloring of a graph is a {\it total monochromatically-connecting coloring} ({\it TMC-coloring}, for short) if any two vertices of the graph are connected by a path whose edges and internal vertices have the same color. For a connected graph G, the {\it total monochromatic connection number}, denoted by tmc(G), is defined as the maximum number of colors used in a TMC-coloring of G. In this paper, we study two kinds of Erd\H{o}s-Gallai-type problems for tmc(G) and completely solve them.

          Related collections

          Most cited references6

          • Record: found
          • Abstract: not found
          • Article: not found

          Spanning trees with many leaves

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Total rainbow k-connection in graphs

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Total monochromatic connection of graphs

                Bookmark

                Author and article information

                Journal
                2016-12-16
                Article
                1612.05381
                f9d661cc-5b84-47ab-bbd5-a58b5e4b3f91

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                05C15, 05C35, 05C38, 05C40
                8 pages
                math.CO

                Combinatorics
                Combinatorics

                Comments

                Comment on this article