Primal graphs with small degrees

Phyllis Z. Chinn; R. Bruce Richter; Miroslaw Truszczynski

doi:10.1016/0012-365X(91)90133-M

Primal graphs with small degrees

Phyllis Z. Chinn, R. Bruce Richter, Miroslaw Truszczynski

Computer Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

It has previously been shown that there is a unique set Π of primal graphs such that every graph has an edge-decomposition into non-isomorphic elements of Π and that the only decomposition of an element of Π into non-isomorphic elements of Π is the obvious one. Here it is shown that there are infinitely many elements of Π even among graphs having a relatively simple structure. On the other hand, within this same class of graphs, we show that 'most' of them are not primal.

Original language	English
Pages (from-to)	237-248
Number of pages	12
Journal	Discrete Mathematics
Volume	87
Issue number	3
DOIs	https://doi.org/10.1016/0012-365X(91)90133-M
State	Published - Feb 22 1991

Bibliographical note

Funding Information:
The second author conducteds ome of this researchw hile at the Ohio State University on a postdoctorals cholarshipf rom the Natural Sciencesa nd Engineering Research Council of Canada. The support of these institutionsi s gratefully acknowledged.

Funding

The second author conducteds ome of this researchw hile at the Ohio State University on a postdoctorals cholarshipf rom the Natural Sciencesa nd Engineering Research Council of Canada. The support of these institutionsi s gratefully acknowledged.

Funders	Funder number
Natural Sciences and Engineering Research Council of Canada
Ohio State University

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(91)90133-M

Cite this

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title = "Primal graphs with small degrees",

abstract = "It has previously been shown that there is a unique set Π of primal graphs such that every graph has an edge-decomposition into non-isomorphic elements of Π and that the only decomposition of an element of Π into non-isomorphic elements of Π is the obvious one. Here it is shown that there are infinitely many elements of Π even among graphs having a relatively simple structure. On the other hand, within this same class of graphs, we show that 'most' of them are not primal.",

author = "Chinn, \{Phyllis Z.\} and Richter, \{R. Bruce\} and Miroslaw Truszczynski",

note = "Funding Information: The second author conducteds ome of this researchw hile at the Ohio State University on a postdoctorals cholarshipf rom the Natural Sciencesa nd Engineering Research Council of Canada. The support of these institutionsi s gratefully acknowledged.",

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N2 - It has previously been shown that there is a unique set Π of primal graphs such that every graph has an edge-decomposition into non-isomorphic elements of Π and that the only decomposition of an element of Π into non-isomorphic elements of Π is the obvious one. Here it is shown that there are infinitely many elements of Π even among graphs having a relatively simple structure. On the other hand, within this same class of graphs, we show that 'most' of them are not primal.

AB - It has previously been shown that there is a unique set Π of primal graphs such that every graph has an edge-decomposition into non-isomorphic elements of Π and that the only decomposition of an element of Π into non-isomorphic elements of Π is the obvious one. Here it is shown that there are infinitely many elements of Π even among graphs having a relatively simple structure. On the other hand, within this same class of graphs, we show that 'most' of them are not primal.

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ER -

Primal graphs with small degrees

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

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