TY - JOUR
T1 - Long cycles in unbalanced bipartite graphs
AU - Chiba, Shuya
AU - Fujisawa, Jun
AU - Tsugaki, Masao
AU - Yamashita, Tomoki
PY - 2012/6/6
Y1 - 2012/6/6
N2 - Let G[X,Y] be a 2-connected bipartite graph with |X|<|Y|. For S⊆V(G), we define δ(S;G):=min dG(v):v∈S. We define σ1 ,1(G):=min dG(x)+ dG(y):x∈X, y∈Y,xy∉E(G) and σ2(X):=min dG(x)+ dG(y):x,y∈X,x≠y. We denote by c(G) the length of a longest cycle in G. Jackson [B. Jackson, Long cycles in bipartite graphs, J. Combin. Theory Ser. B 38 (1985) 118-131] proved that c(G),1(G)-2,2 σ2(X)-4, 2|Y|.
AB - Let G[X,Y] be a 2-connected bipartite graph with |X|<|Y|. For S⊆V(G), we define δ(S;G):=min dG(v):v∈S. We define σ1 ,1(G):=min dG(x)+ dG(y):x∈X, y∈Y,xy∉E(G) and σ2(X):=min dG(x)+ dG(y):x,y∈X,x≠y. We denote by c(G) the length of a longest cycle in G. Jackson [B. Jackson, Long cycles in bipartite graphs, J. Combin. Theory Ser. B 38 (1985) 118-131] proved that c(G),1(G)-2,2 σ2(X)-4, 2|Y|.
KW - Bipartite graph
KW - Degree
KW - Longest cycle
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U2 - 10.1016/j.disc.2012.02.019
DO - 10.1016/j.disc.2012.02.019
M3 - Article
AN - SCOPUS:84858206034
VL - 312
SP - 1857
EP - 1862
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
IS - 11
ER -