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LI Shi-yin, BAI Yun, DONG Qian, REN Han. Unicyclic subgraphs in 2-connected graphs(Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2008, (3): 37-44,1.
Citation:
LI Shi-yin, BAI Yun, DONG Qian, REN Han. Unicyclic subgraphs in 2-connected graphs(Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2008, (3): 37-44,1.
LI Shi-yin, BAI Yun, DONG Qian, REN Han. Unicyclic subgraphs in 2-connected graphs(Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2008, (3): 37-44,1.
Citation:
LI Shi-yin, BAI Yun, DONG Qian, REN Han. Unicyclic subgraphs in 2-connected graphs(Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2008, (3): 37-44,1.
This paper proved the following results:(1) The ⊙-graph of a 2-connected graph is 2(p-1) connected; (2) if a 2-connected graph G has two unicyclic spanning subgraphs and the number of one-valent vertices of these two subgraphs are respectively m and n (mn), then for any integer k:m≦k≦n,there exist at least 2(p-1) unicyclic subgraphs of graph G whick have k one-valent vertices. Here, p is the dimension of the cycle space of G.
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