2003
DOI: 10.1016/s0166-218x(02)00571-1
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On linear and circular structure of (claw, net)-free graphs

Abstract: We prove that every (claw, net)-free graph contains an induced doubly dominating cycle or a dominating pair. Moreover, using LexBFS we present a linear time algorithm which, for a given (claw, net)-free graph, ÿnds either a dominating pair or an induced doubly dominating cycle. We show also how one can use structural properties of (claw, net)-free graphs to solve e ciently the domination, independent domination, and independent set problems on these graphs. ?

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Cited by 29 publications
(18 citation statements)
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“…Also note that CN-free graphs are exactly the Hamiltonian-hereditary graphs [13] (was cited in [4]). CN-free graphs turn out to be closely related to AT-free graphs form their structure properties [4]. There are, however, few results about the structure of these graphs [4].…”
Section: Introductionmentioning
confidence: 99%
See 3 more Smart Citations
“…Also note that CN-free graphs are exactly the Hamiltonian-hereditary graphs [13] (was cited in [4]). CN-free graphs turn out to be closely related to AT-free graphs form their structure properties [4]. There are, however, few results about the structure of these graphs [4].…”
Section: Introductionmentioning
confidence: 99%
“…CN-free graphs turn out to be closely related to AT-free graphs form their structure properties [4]. There are, however, few results about the structure of these graphs [4]. In [4] the authors give results on the linear and circular structure of CN-free graphs.…”
Section: Introductionmentioning
confidence: 99%
See 2 more Smart Citations
“…G is said to be H-free, if H is not a subgraph of G. If H is a set of graphs, G is H-free if G is H free for all H ∈ H. There is some literature concerning {claw, net}-free graphs, dealing with domination and hamiltonicity problems: It was shown by Damaschke [12] that a connected graph is {claw, net}-free iff each of its connected induced subgraphs has a hamiltonian path. Later, Brandstädt and Dragan [13] studied {claw, net}-free graphs in view of their linear and circular structure. They proved that a connected {claw, net}-free graph either has a doubly dominating induced cycle or a dominating pair, i.e.…”
Section: Introductionmentioning
confidence: 99%