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- W1577216066 abstract "This chapter provides an overview of perfect graph theorem. A version of the perfect graph theorem says, “Let A be a (0, l)-matrix such that the linear program yA w, y 0, min 1. y (where 1 = (1,. . . , 1)) always has an integer solution vector y whenever w is a (0, 1)-vector, then this program always has an integer solution vector y whenever w is a non-negative integer vector. The chapter discusses some well-known integer-valued functions of an arbitrary graph. Another perfect graph theorem says that if G is γ-perfect (or π-perfect), then G is perfect. A stronger form, one that is still open, asserts that G is perfect if and only if neither G nor its complement G contains an odd hole. The pluperfect graph theorem is that if G is γ-pluperfect (or π-pluperfect), then G is pluperfect. Thus, to prove the perfect graph theorem, it would suffice to show that if G is π-perfect, then G is also π-pluperfect." @default.
- W1577216066 created "2016-06-24" @default.
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- W1577216066 date "1973-01-01" @default.
- W1577216066 modified "2023-10-16" @default.
- W1577216066 title "On the Perfect Graph Theorem" @default.
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- W1577216066 doi "https://doi.org/10.1016/b978-0-12-358350-5.50006-3" @default.
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