The Number of Vertices of Degree k in a Minimally k-Edge-Connected Graph
Let G be a minimally k-edge-connected simple graph and u(G) be the number of vertices of degree k in G. It is proved that (i) u(G) ≥ ((2k - 1)/2(2k + 3)) |G| + (14k + l)/2(2k+3) for even k ≥ 6 and u(G) ≥ |G|/4 + 13/4 for k = 4, and (ii) u(G) ≥ ((2k − 1)/2(2k + 5)) |G| + (10k + l)/(2k + 5) for odd k...
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| Veröffentlicht in: | Journal of combinatorial theory. Series B 1993-07, Vol.58 (2), p.225-239 |
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| container_title | Journal of combinatorial theory. Series B |
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| creator | Cai, M.C. |
| description | Let G be a minimally k-edge-connected simple graph and u(G) be the number of vertices of degree k in G. It is proved that (i) u(G) ≥ ((2k - 1)/2(2k + 3)) |G| + (14k + l)/2(2k+3) for even k ≥ 6 and u(G) ≥ |G|/4 + 13/4 for k = 4, and (ii) u(G) ≥ ((2k − 1)/2(2k + 5)) |G| + (10k + l)/(2k + 5) for odd k ≥ 7 and u(G) ≥ |G|/5 + 24/5 for k = 5, where |G| denotes the number of vertices of G. |
| doi_str_mv | 10.1006/jctb.1993.1039 |
| format | Article |
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It is proved that (i) u(G) ≥ ((2k - 1)/2(2k + 3)) |G| + (14k + l)/2(2k+3) for even k ≥ 6 and u(G) ≥ |G|/4 + 13/4 for k = 4, and (ii) u(G) ≥ ((2k − 1)/2(2k + 5)) |G| + (10k + l)/(2k + 5) for odd k ≥ 7 and u(G) ≥ |G|/5 + 24/5 for k = 5, where |G| denotes the number of vertices of G.</abstract><pub>Elsevier Inc</pub><doi>10.1006/jctb.1993.1039</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
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| source | ScienceDirect Journals (5 years ago - present); EZB-FREE-00999 freely available EZB journals |
| title | The Number of Vertices of Degree k in a Minimally k-Edge-Connected Graph |
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