On vertex b-critical trees
A b-coloring is a proper coloring of the vertices of a graph such that each color class has a vertex that has neighbors of all other colors. The b-chromatic number of a graph G is the largest k such that G admits a b-coloring with k colors. A graph G is b-critical if the removal of any vertex of G d...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2013-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol33/1/art/opuscula_math_3302.pdf |
| _version_ | 1819084372432650240 |
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| author | Mostafa Blidia Noureddine Ikhlef Eschouf Frédéric Maffray |
| author_facet | Mostafa Blidia Noureddine Ikhlef Eschouf Frédéric Maffray |
| author_sort | Mostafa Blidia |
| collection | DOAJ |
| description | A b-coloring is a proper coloring of the vertices of a graph such that each color class has a vertex that has neighbors of all other colors. The b-chromatic number of a graph G is the largest k such that G admits a b-coloring with k colors. A graph G is b-critical if the removal of any vertex of G decreases the b-chromatic number. We prove various properties of b-critical trees. In particular, we characterize b-critical trees. |
| first_indexed | 2024-12-21T20:47:25Z |
| format | Article |
| id | doaj.art-4c83418f546142f8803586a4efd66e56 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-21T20:47:25Z |
| publishDate | 2013-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-4c83418f546142f8803586a4efd66e562022-12-21T18:50:47ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742013-01-013311928http://dx.doi.org/10.7494/OpMath.2013.33.1.193302On vertex b-critical treesMostafa Blidia0Noureddine Ikhlef Eschouf1Frédéric Maffray2University of Blida, LAMDA-RO, Department of Mathematics, B.P. 270, Blida, AlgeriaDr. Yahia Fares University of Médéa, Faculty of Science and Technology, Department of G.E.I., AlgeriaGrenoble-INP, Université Joseph Fourier, C.N.R.S, Laboratoire G-SCOP, Grenoble, FranceA b-coloring is a proper coloring of the vertices of a graph such that each color class has a vertex that has neighbors of all other colors. The b-chromatic number of a graph G is the largest k such that G admits a b-coloring with k colors. A graph G is b-critical if the removal of any vertex of G decreases the b-chromatic number. We prove various properties of b-critical trees. In particular, we characterize b-critical trees.http://www.opuscula.agh.edu.pl/vol33/1/art/opuscula_math_3302.pdfb-coloringb-critical graphsb-critical trees |
| spellingShingle | Mostafa Blidia Noureddine Ikhlef Eschouf Frédéric Maffray On vertex b-critical trees Opuscula Mathematica b-coloring b-critical graphs b-critical trees |
| title | On vertex b-critical trees |
| title_full | On vertex b-critical trees |
| title_fullStr | On vertex b-critical trees |
| title_full_unstemmed | On vertex b-critical trees |
| title_short | On vertex b-critical trees |
| title_sort | on vertex b critical trees |
| topic | b-coloring b-critical graphs b-critical trees |
| url | http://www.opuscula.agh.edu.pl/vol33/1/art/opuscula_math_3302.pdf |
| work_keys_str_mv | AT mostafablidia onvertexbcriticaltrees AT noureddineikhlefeschouf onvertexbcriticaltrees AT fredericmaffray onvertexbcriticaltrees |