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A graph is defined to be an atom if no minimal vertex separator induces a complete subgraph; thus, atoms are the graphs that are immune to clique separator decomposition. Atoms are characterized here in two ways: first using generalized vertex elimination schemes, and then as generalizations of 2-connected unichord-free graphs (the graphs in which every minimal vertex separator induces an edgeless subgraph).
Terry A. McKee. "Characterizing Atoms that Result from Decomposition by Clique Separators." Discussiones Mathematicae Graph Theory 37.3 (2017): 587-594. <http://eudml.org/doc/288422>.
@article{TerryA2017, abstract = {A graph is defined to be an atom if no minimal vertex separator induces a complete subgraph; thus, atoms are the graphs that are immune to clique separator decomposition. Atoms are characterized here in two ways: first using generalized vertex elimination schemes, and then as generalizations of 2-connected unichord-free graphs (the graphs in which every minimal vertex separator induces an edgeless subgraph).}, author = {Terry A. McKee}, journal = {Discussiones Mathematicae Graph Theory}, keywords = {clique separator; minimal separator; unichord-free graph}, language = {eng}, number = {3}, pages = {587-594}, title = {Characterizing Atoms that Result from Decomposition by Clique Separators}, url = {http://eudml.org/doc/288422}, volume = {37}, year = {2017}, }
TY - JOUR AU - Terry A. McKee TI - Characterizing Atoms that Result from Decomposition by Clique Separators JO - Discussiones Mathematicae Graph Theory PY - 2017 VL - 37 IS - 3 SP - 587 EP - 594 AB - A graph is defined to be an atom if no minimal vertex separator induces a complete subgraph; thus, atoms are the graphs that are immune to clique separator decomposition. Atoms are characterized here in two ways: first using generalized vertex elimination schemes, and then as generalizations of 2-connected unichord-free graphs (the graphs in which every minimal vertex separator induces an edgeless subgraph). LA - eng KW - clique separator; minimal separator; unichord-free graph UR - http://eudml.org/doc/288422 ER -