TY - JOUR

T1 - Almost self-complementary factors of complete bipartite graphs

AU - Fronček, Dalibor

PY - 1997/4/15

Y1 - 1997/4/15

N2 - A complete bipartite graph without one edge, K̃n, m, is called almost complete bipartite graph. A graph K̃2n+1, 2m+1 that can be decomposed into two isomorphic factors with a given diameter d is called d-isodecomposable. We prove that K̃2n+1, 2m+1 is d-isodecomposable only if d = 3, 4, 5, 6 or ∞ and completely determine all d-isodecomposable almost complete bipartite graphs for each diameter. For d = ∞ we, moreover, present all classes of possible disconnected factors.

AB - A complete bipartite graph without one edge, K̃n, m, is called almost complete bipartite graph. A graph K̃2n+1, 2m+1 that can be decomposed into two isomorphic factors with a given diameter d is called d-isodecomposable. We prove that K̃2n+1, 2m+1 is d-isodecomposable only if d = 3, 4, 5, 6 or ∞ and completely determine all d-isodecomposable almost complete bipartite graphs for each diameter. For d = ∞ we, moreover, present all classes of possible disconnected factors.

KW - Graph decompositions

KW - Isomorphic factors

KW - Self-complementary graphs

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U2 - 10.1016/S0012-365X(96)00237-3

DO - 10.1016/S0012-365X(96)00237-3

M3 - Article

AN - SCOPUS:0039382459

SN - 0012-365X

VL - 167-168

SP - 317

EP - 327

JO - Discrete Mathematics

JF - Discrete Mathematics

ER -