All about Clique-Colouring encoded as equalities

Proof Systems

• The size complexity of Clique-Colouring encoded as equalities in Resolution is exponential
  • Source: CliqueColouringeq → CP → uCP → Res
• The size complexity of Clique-Colouring encoded as equalities in Truth table is exponential
  • Source: CliqueColouringeq → CP → tlCP → tlRes → ttp
• The size complexity of Clique-Colouring encoded as equalities in Tree-like resolution is exponential
  • Source: CliqueColouringeq → CP → tlCP → tlRes
• The size complexity of Clique-Colouring encoded as equalities in Regular resolution is exponential
  • Source: CliqueColouringeq → CP → uCP → Res → regRes
• The size complexity of Clique-Colouring encoded as equalities in Ordered resolution is exponential
  • Source: CliqueColouringeq → CP → uCP → Res → regRes → ordRes
• The size complexity of Clique-Colouring encoded as equalities in Pool resolution is exponential
  • Source: CliqueColouringeq → CP → uCP → Res → poolRes
• The size complexity of Clique-Colouring encoded as equalities in Linear resolution is exponential
  • Source: CliqueColouringeq → CP → uCP → Res → linRes
• The size complexity of Clique-Colouring encoded as equalities in Reversible resolution is exponential
  • Source: CliqueColouringeq → CP → uCP → Res → revRes
• The size complexity of Clique-Colouring encoded as equalities in Cutting Planes is exponential
  • Source: FHL16 Semantic Versus Syntactic Cutting Planes.
• The size complexity of Clique-Colouring encoded as equalities in Tree-like Cutting Planes is exponential
  • Source: CliqueColouringeq → CP → tlCP
• The size complexity of Clique-Colouring encoded as equalities in Cutting Planes with Unary Coefficients is exponential
  • Source: CliqueColouringeq → CP → uCP
• The size complexity of Clique-Colouring encoded as equalities in Semantic Cutting Planes is polynomial
  • Source: [citation needed]
• The size complexity of Clique-Colouring encoded as equalities in Cutting Planes with Saturation is exponential
  • Source: CliqueColouringeq → CP → uCP → Res → saturationCP
• The size complexity of Clique-Colouring encoded as equalities in Stabbing Planes is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Stabbing Planes with Unary Coefficients is exponential
  • Source: CliqueColouringeq → CP → uSP
• The size complexity of Clique-Colouring encoded as equalities in Res(CP) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Res(LP) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Res(CP) with unary coefficients is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Res(LP) with unary coefficients is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Res(L\(\&\)P) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Res(L\(\&\)P) with unary coefficients is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Semantic degree-k threshold system, treelike version is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Polynomial Calculus over \(\mathbb{F}_2\) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Nullstellensatz over \(\mathbb{F}_2\) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in unary ResLin over \(\mathbb{Q}\), ResLin, Resolution over linear equations over rationals is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in ResLin over \(\mathbb{F}_2\), Res(\(\oplus\)) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Tree-like ResLin over \(\mathbb{F}_2\), treelike Res(\(\oplus\)) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Polynomial Calculus over \(\mathbb{Q}\) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Nullstellensatz over \(\mathbb{Q}\) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Hitting is exponential
  • Source: CliqueColouringeq → CP → tlCP → tlRes → hit
• The size complexity of Clique-Colouring encoded as equalities in Lift and Project is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Lift and Project with unary coefficients is exponential
  • Source: CliqueColouringeq → CP → uCP → uL&P
• The size complexity of Clique-Colouring encoded as equalities in Positivstellensatz Calculus is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Positivstellensatz is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Lovász--Schrijver (LS) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Lovász--Schrijver with squares (LS\(_+^\infty\)), unbounded degree is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Cone Proof System is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in tl Lovász--Schrijver (LS) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Lovász--Schrijver with squares (LS\(_+\)) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Lovász--Schrijver with squares (LS\(_+^d\)), bounded degree, treelike is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in static Lovász--Schrijver (static LS) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in static Lovász--Schrijver, with squares of linear functions (static LS\(_+\)) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in static Lovász--Schrijver, with squares of linear functions (static LS\(_+^n\)) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Sum of Squares (Lasserre) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Sherali--Adams is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Circular resolution is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Unary Sherali--Adams is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Ideal Proof System is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Extended Frege is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Extended resolution is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Frege is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in \(\mathrm{AC}^0\)-Frege is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in k-DNF Resolution is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in \(\mathrm{TC}^0\)-Frege is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in \(\mathrm{AC}^0\)-Frege with mod 2 axioms is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in \(\mathrm{AC}^0\)-Frege with mod 2 gates is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in OBDD(join,weakening) is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in LK is [missing?]
• The size complexity of Clique-Colouring encoded as equalities in Zermelo-Fraenkl Set Theory with the Axiom of Choice is [missing?]

This database is still incomplete; missing data may indicate either the information was not yet recorded or an open problem. Users are encouraged to contribute missing proof systems and/or relations at https://gitlab.com/proofcomplexityzoo/zoo.

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