Erdős-Gallai-Type Results for Total Monochromatic Connection of Graphs
A graph is said to be total-colored if all the edges and the vertices of the graph are colored. A total-coloring of a graph is a total monochromatically-connecting coloring (TMC-coloring, for short) if any two vertices of the graph are connected by a path whose edges and internal vertices have the s...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2019-11-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.2095 |
| _version_ | 1797713175906353152 |
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| author | Jiang Hui Li Xueliang Zhang Yingying |
| author_facet | Jiang Hui Li Xueliang Zhang Yingying |
| author_sort | Jiang Hui |
| collection | DOAJ |
| description | A graph is said to be total-colored if all the edges and the vertices of the graph are colored. A total-coloring of a graph is a total monochromatically-connecting coloring (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 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 Erdős-Gallai-type problems for tmc(G) and completely solve them. |
| first_indexed | 2024-03-12T07:32:42Z |
| format | Article |
| id | doaj.art-d28548f76bed40f7801f2f4acc76554c |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T07:32:42Z |
| publishDate | 2019-11-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-d28548f76bed40f7801f2f4acc76554c2023-09-02T21:43:04ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922019-11-0139477578510.7151/dmgt.2095dmgt.2095Erdős-Gallai-Type Results for Total Monochromatic Connection of GraphsJiang Hui0Li Xueliang1Zhang Yingying2Center for Combinatorics and LPMC, Nankai University, Tianjin300071, ChinaCenter for Combinatorics and LPMC, Nankai University, Tianjin300071, ChinaCenter for Combinatorics and LPMC, Nankai University, Tianjin300071, ChinaA graph is said to be total-colored if all the edges and the vertices of the graph are colored. A total-coloring of a graph is a total monochromatically-connecting coloring (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 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 Erdős-Gallai-type problems for tmc(G) and completely solve them.https://doi.org/10.7151/dmgt.2095total-colored graphtotal monochromatic connectionerdős- gallai-type problem05c1505c3505c3805c40 |
| spellingShingle | Jiang Hui Li Xueliang Zhang Yingying Erdős-Gallai-Type Results for Total Monochromatic Connection of Graphs Discussiones Mathematicae Graph Theory total-colored graph total monochromatic connection erdős- gallai-type problem 05c15 05c35 05c38 05c40 |
| title | Erdős-Gallai-Type Results for Total Monochromatic Connection of Graphs |
| title_full | Erdős-Gallai-Type Results for Total Monochromatic Connection of Graphs |
| title_fullStr | Erdős-Gallai-Type Results for Total Monochromatic Connection of Graphs |
| title_full_unstemmed | Erdős-Gallai-Type Results for Total Monochromatic Connection of Graphs |
| title_short | Erdős-Gallai-Type Results for Total Monochromatic Connection of Graphs |
| title_sort | erdos gallai type results for total monochromatic connection of graphs |
| topic | total-colored graph total monochromatic connection erdős- gallai-type problem 05c15 05c35 05c38 05c40 |
| url | https://doi.org/10.7151/dmgt.2095 |
| work_keys_str_mv | AT jianghui erdosgallaityperesultsfortotalmonochromaticconnectionofgraphs AT lixueliang erdosgallaityperesultsfortotalmonochromaticconnectionofgraphs AT zhangyingying erdosgallaityperesultsfortotalmonochromaticconnectionofgraphs |