Minimal vertex degree sum of a 3-path in plane maps

• Autorzy: O.V. Borodin
• Języki publikacji: EN

Abstrakty

EN

Let wₖ be the minimum degree sum of a path on k vertices in a graph. We prove for normal plane maps that: (1) if w₂ = 6, then w₃ may be arbitrarily big, (2) if w₂ < 6, then either w₃ ≤ 18 or there is a ≤ 15-vertex adjacent to two 3-vertices, and (3) if w₂ < 7, then w₃ ≤ 17.

Słowa kluczowe

EN

planar graph; structure; degree; path; weight

Kategorie tematyczne

• 05C10: Planar graphs; geometric and topological aspects of graph theory

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1997
• Tom: 17
• Numer: 2
• Strony: 279-284

Daty

wydano

1997

otrzymano

1996-04-23

poprawiono

1997-03-04

Twórcy

autor

O.V. Borodin

• Novosibirsk State University, Novosibirsk, 630090, Russia

Bibliografia

• [1] O.V. Borodin, Solution of Kotzig's and Grünbaum's problems on the separability of a cycle in plane graph, (in Russian), Matem. zametki 48 (6) (1989) 9-12.
• [2] O.V. Borodin, Triangulated 3-polytopes without faces of low weight, submitted.
• [3] H. Enomoto and K. Ota, Properties of 3-connected graphs, preprint (April 21, 1994).
• [4] K. Ando, S. Iwasaki and A. Kaneko, Every 3-connected planar graph has a connected subgraph with small degree sum I, II (in Japanese), Annual Meeting of Mathematical Society of Japan, 1993.
• [5] Ph. Franklin, The four colour problem, Amer. J. Math. 44 (1922) 225-236, doi: 10.2307/2370527.
• [6] S. Jendrol', Paths with restricted degrees of their vertices in planar graphs, submitted.
• [7] S. Jendrol', A structural property of 3-connected planar graphs, submitted.
• [8] A. Kotzig, Contribution to the theory of Eulerian polyhedra, (in Russian), Mat. Čas. 5 (1955) 101-103.

Identyfikatory

DOI

10.7151/dmgt.1055