S. Hougardy, F. Ma ray, and A. Sebo, private communication (1997) Home/Search Document Not in Database Summary Related Articles Check |
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The Classes of Critically and Anticritically Perfect Graphs - Wagler (2000) (Correct)
....graphs having minimal counterexamples in A PERF and C PERF is the class of preperfect graphs. Hammer and Maffray [9] presented an in nite sequence of perfect but minimally non preperfect graphs. A di erent sequence of such graphs was found (but not published) by Hougardy, Maffray, and Seb o [15]. All these graphs are line graphs of special bipartite graphs. Motivated by this observation, minimally non preperfect graphs with small maximum degree have been investigated in [27] and characterized for maximum degree 4 as follows. Theorem 6.6 (Tuza and Wagler [27] A graph of maximum degree ....
S. Hougardy, F. Ma ray, and A. Sebo, private communication (1997)
The Classes of Critically and Anticritically Perfect Graphs - Wagler (2000) (Correct)
....path of even length 4. i.e. the graph itself is anticritically perfect and, therefore, a singleton in the graph of all perfect graphs. As we will see later, critically and anticritically perfect graphs are not rare, albeit the strange requirements to be satis ed. A computer search of Hougardy [13] provides an enumeration of small critically perfect graphs. Further examples are presented throughout the next section. Figure 2 Theorem 3.1 (Hougardy [13] No critically perfect graphs with fewer than 9 nodes exist. On 9 and 10 nodes there are precisely 3 and 10 critically perfect graphs, ....
....critically and anticritically perfect graphs are not rare, albeit the strange requirements to be satis ed. A computer search of Hougardy [13] provides an enumeration of small critically perfect graphs. Further examples are presented throughout the next section. Figure 2 Theorem 3. 1 (Hougardy [13]) No critically perfect graphs with fewer than 9 nodes exist. On 9 and 10 nodes there are precisely 3 and 10 critically perfect graphs, respectively. Theorem 3.1 obviously remains true if critically perfect is replaced by anticritically perfect . Figure 3 shows the three critically perfect ....
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S. Hougardy, private communication (1996)
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