Geodesic
Hamiltonicity and pancyclicity of superclasses of claw-free graphs
Filomat, Tome 37 (2023) no. 14, p. 4771

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DOI

A graph G is called to be fully cycle extendable graph [3] if each vertex of G belongs to a triangle and for any cycle C with |V(C)| |V(G)| there exists a cycle C ′ in G such that V(C) ⊂ V(C ′) and |V(C ′)| = |V(C)|+1. In this paper, we show that every graph G that is triangularly connected, partly claw-free and {K 1,4 , K 4 }-free is fully cycle extendable graph if its claw centers set is P 4-free. This paper generalizes the concept of Hendry fully cycle extendable graph [3] for the largest superclass of partly claw-free graphs defined by Abbas and Benmeziane [1].
DOI : 10.2298/FIL2314771S
Classification : 05C45, 05C75
Keywords: K1, 4-free graphs, partly claw-free graphs, triangularly connected graphs, fully cycle extendable graphs 
Abdelkader Sahraoui; Zineb Benmeziane. Hamiltonicity and pancyclicity of superclasses of claw-free graphs. Filomat, Tome 37 (2023) no. 14, p. 4771 . doi: 10.2298/FIL2314771S
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     title = {Hamiltonicity and pancyclicity of superclasses of claw-free graphs},
     journal = {Filomat},
     pages = {4771 },
     year = {2023},
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     number = {14},
     doi = {10.2298/FIL2314771S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2314771S/}
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