Forbidden triples for perfect matchings

Ota, Katsuhiro; Plummer, Michael D.; Saito, Akira

doi:10.1002/jgt.20529

Cited by 7 publications

(3 citation statements)

References 10 publications

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“…Given a collection F of graphs, a graph G is F-free if G contains no induced subgraph isomorphic to an element of F, and the elements of F are forbidden subgraphs for the class of F-free graphs. Recently interest has developed in determining which small sets of induced subgraphs can be forbidden to produce graphs having special properties, such as 3-colorability [23], traceability [14], k-connected Hamiltonian [6], or the containment of a Hamiltonian cycle [8], 2-factor [1], or perfect matching [11,12,20,21].…”

Section: Introductionmentioning

confidence: 99%

Minimal forbidden sets for degree sequence characterizations

Barrus

Hartke

2015

Discrete Mathematics

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Given a set $\mathcal{F}$ of graphs, a graph $G$ is $\mathcal{F}$-free if $G$ does not contain any member of $\mathcal{F}$ as an induced subgraph. Barrus, Kumbhat, and Hartke [M. D. Barrus, M. Kumbhat, and S. G. Hartke, Graph classes characterized both by forbidden subgraphs and degree sequences, J. Graph Theory (2008), no. 2, 131--148] called $\mathcal{F}$ a degree-sequence-forcing (DSF) set if, for each graph $G$ in the class $\mathcal{C}$ of $\mathcal{F}$-free graphs, every realization of the degree sequence of $G$ is also in $\mathcal{C}$. A DSF set is minimal if no proper subset is also DSF. In this paper, we present new properties of minimal DSF sets, including that every graph is in a minimal DSF set and that there are only finitely many DSF sets of cardinality $k$. Using these properties and a computer search, we characterize the minimal DSF triples.Comment: 19 pages, 4 figure

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Section: Introductionmentioning

confidence: 99%

Minimal forbidden sets for degree sequence characterizations

Barrus

Hartke

2015

Discrete Mathematics

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“…According to Theorem 2, as long as we consider exactly one forbidden subgraph for the existence of a perfect matching, Theorem 1 gives a complete solution, even if we allow a finite number of exceptions (for studies on relationships between the existence of a perfect matching and two or more forbidden subgraphs, we refer the reader to [5,6,8,9]).…”

Section: Introductionmentioning

confidence: 99%

Perfect Matchings Avoiding Several Independent Edges in a Star‐Free Graph

Egawa

Furuya

2015

Journal of Graph Theory

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Abstract:In Aldred and Plummer (Discrete Math 197/198 (1999) [29][30][31][32][33][34][35][36][37][38][39][40] proved that every m-connected K 1,m−2k−l +2 -free graph of even order has a perfect matching M with F 1 ⊆ M and M ∩ F 2 = ∅, where F 1 and F 2 are prescribed disjoint sets of independent edges with |F 1 | = k and, then the star-free condition in the above result is best possible. In this paper, forwe prove a refinement of the result in which the condition is replaced by the weaker condition that G is K 1, m−2k+2 2 -free (note that the new condition does not depend on l ). We also show that if m is even and either k ≥ 1 or l ≤ 3m 4 , then for m-connected graphs G with sufficiently large order, one can replace the condition by the still weaker condition that G is K 1, m−2k+4 2

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“…Recently, similar questions related to the existence of perfect matchings and 2-factors have been studied. We refer the interested reader to [27,31] and [2,23,28], respectively, for more details.…”

Section: Theorem 72 (Faudree and Gould [24]) Let R And S Be Connectmentioning

confidence: 99%

Subgraph conditions for Hamiltonian properties of graphs

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Forbidden triples for perfect matchings

Cited by 7 publications

References 10 publications

Minimal forbidden sets for degree sequence characterizations

Minimal forbidden sets for degree sequence characterizations

Perfect Matchings Avoiding Several Independent Edges in a Star‐Free Graph

Subgraph conditions for Hamiltonian properties of graphs

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