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 -