TY - JOUR

T1 - Distance Matching Extension in Cubic Bipartite Graphs

AU - Aldred, R. E.L.

AU - Fujisawa, Jun

AU - Saito, Akira

N1 - Funding Information:
J. Fujisawa: work supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B) 16H03952, (C) 17K05349 and (C) 20K03723
Funding Information:
A. Saito: work supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C) 17K00018 and (C) 20K11684.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.

PY - 2021/9

Y1 - 2021/9

N2 - A graph G is said to be distanced matchable if, for any matching M of G in which edges are pairwise at least distance d apart, there exists a perfect matching M∗ of G which contains M. In this paper, we prove the following results: (i) if G is a cubic bipartite graph in which, for each e∈ E(G) , there exist two cycles C1, C2 of length at most d such that E(C1) ∩ E(C2) = { e} , then G is distance d- 1 matchable, and (ii) if G is a planar or projective planar cubic bipartite graph in which, for each e∈ E(G) , there exist two cycles C1, C2 of length at most 6 such that e∈ E(C1) ∩ E(C2) , then G is distance 6 matchable.

AB - A graph G is said to be distanced matchable if, for any matching M of G in which edges are pairwise at least distance d apart, there exists a perfect matching M∗ of G which contains M. In this paper, we prove the following results: (i) if G is a cubic bipartite graph in which, for each e∈ E(G) , there exist two cycles C1, C2 of length at most d such that E(C1) ∩ E(C2) = { e} , then G is distance d- 1 matchable, and (ii) if G is a planar or projective planar cubic bipartite graph in which, for each e∈ E(G) , there exist two cycles C1, C2 of length at most 6 such that e∈ E(C1) ∩ E(C2) , then G is distance 6 matchable.

KW - 05C10

KW - 05C70

KW - Cubic bipartite graphs

KW - Distance restricted matching extension

KW - Planar graphs

KW - Projective planar graphs

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U2 - 10.1007/s00373-021-02295-9

DO - 10.1007/s00373-021-02295-9

M3 - Article

AN - SCOPUS:85103219256

VL - 37

SP - 1793

EP - 1806

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 5

ER -