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Almost claw‐free graphs
Author(s) -
Ryjáček Zdeněk
Publication year - 1994
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190180505
Subject(s) - claw , combinatorics , mathematics , graph , discrete mathematics , biology , ecology
We say that G is almost claw‐free if the vertices that are centers of induced claws ( K 1,3 ) in G are independent and their neighborhoods are 2‐dominated. Clearly, every claw‐free graph is almost claw‐free. It is shown that (i) every even connected almost claw‐free graph has a perfect matching and (ii) every nontrivial locally connected K 1,4 ‐free almost claw‐free graph is fully cycle extendable.