Fan-type theorem for path-connectivity |
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Authors: | Akira Saito |
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Institution: | (1) Department of Mathematics, Nihon University, Sakurajosui 3-25-40 Setagaya-ku, 156 Tokyo, JAPAN |
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Abstract: | A graphG is said to bek-path-connected if every pair of distinct vertices inG are joined by a path of length at leastk. We prove that if max{deg
G
x
, deg
G
y
} k for every pair of verticesx,y withd
G
(x,y)=2 in a 2-connected graphG, whered
G
(x,y) is the distance betweenx andy inG, thenG isk-path-connected. |
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Keywords: | 05C38 |
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