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Note as to inclusion-minimal non-Bondy systems

T. J. Kepka, P. C. Nemec, J. D. Phillips

Abstract

Let $S$ be a finite set, $s=|S|\ge6$. Given a non-negative integer $t$, there exists an inclusion-minimal non-Bondy system $\mathscr{A}$ of size $t$ on $S$ if and only if $s+1\le t\le2s$.

Note as to inclusion-minimal non-Bondy systems

Abstract

Let be a finite set, . Given a non-negative integer , there exists an inclusion-minimal non-Bondy system of size on if and only if .
Paper Structure (4 sections, 20 theorems)

This paper contains 4 sections, 20 theorems.

Table of Contents

  1. Introduction (Bondy Systems)
  2. Introduction (Non-Bondy Systems)
  3. The case $1 \le s \le 6$
  4. Main result

Key Result

Theorem 1.1

(Bondy) If $|\mathscr{A}| \le s (= |S|)$ then $\mathscr{A}$ is a Bondy system.

Theorems & Definitions (34)

  • Theorem 1.1
  • Proposition 1.2
  • Proposition 1.3
  • Proposition 1.4
  • Proposition 2.1
  • Proposition 2.2
  • Proposition 2.3
  • Theorem 2.4
  • proof
  • Example 2.5
  • ...and 24 more