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Discussiones Mathematicae Graph Theory  17(2) (1997)  279-284
DOI: https://doi.org/10.7151/dmgt.1055

MINIMAL VERTEX DEGREE SUM OF A 3-PATH IN PLANE MAPS

O.V. Borodin

Novosibirsk State University
Novosibirsk, 630090, Russia

Abstract

Let w_k 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.

Keywords: planar graph, structure, degree, path, weight.

1991 Mathematics Subject Classification: 05C10.

References

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