TY - GEN

T1 - A Neighborhood Condition for Graphs to Have [a, b]-Factors III

AU - Kano, M.

AU - Matsuda, Haruhide

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2007

Y1 - 2007

N2 - Let a, b, k, and m be positive integers such that 1 ≤a < b and 2 k (b + 1 - m)/a. Let G = (V(G), E(G)) be a graph of order |G|. Suppose that |G| > (a + b)(k(a + b - 1) - 1)/b and |N G (x 1) ∪ N G (x 2)... ∪ N G (xk )| ≥ a|G|/(a + b) for every independent set { x 1, x 2, ..., x k} ⊆ V(G). Then for any subgraph H of G with m edges and δ(G - E(H))≥ a, G has an [a, b]-factor F such that E(H)∩ E(F) = θ. This result is best possible in some sense and it is an extension of the result of Matsuda (Discrete Mathematics 224 (2000) 289-292).

AB - Let a, b, k, and m be positive integers such that 1 ≤a < b and 2 k (b + 1 - m)/a. Let G = (V(G), E(G)) be a graph of order |G|. Suppose that |G| > (a + b)(k(a + b - 1) - 1)/b and |N G (x 1) ∪ N G (x 2)... ∪ N G (xk )| ≥ a|G|/(a + b) for every independent set { x 1, x 2, ..., x k} ⊆ V(G). Then for any subgraph H of G with m edges and δ(G - E(H))≥ a, G has an [a, b]-factor F such that E(H)∩ E(F) = θ. This result is best possible in some sense and it is an extension of the result of Matsuda (Discrete Mathematics 224 (2000) 289-292).

KW - Factor

KW - Neighborhood union

KW - [a, b]-factor

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U2 - 10.1007/978-3-540-70666-3_8

DO - 10.1007/978-3-540-70666-3_8

M3 - Conference contribution

AN - SCOPUS:49949116358

SN - 3540706658

SN - 9783540706656

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 70

EP - 78

BT - Discrete Geometry, Combinatorics and Graph Theory 7th China-Japan Conference, CJCDGCGT 2005, Tianjin, China, November 18-20, 2005, Xi'an, China, November 22-24, 2005, Revised Selected Papers

T2 - 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005

Y2 - 22 November 2005 through 24 November 2005

ER -