Export Conference item Approximate graph colouring and the hollow shadow Abstract: We show that approximate graph colouring is not solved by constantly many levels of the liftand.
c-colourable graph, where 3 ≤ c ≤ d. There is a huge gap in our understanding of this problem. For an n-vertex graph and c = 3, the best known polynomial-time algorithm of Kawarabayashi, Thorup, and Yoneda [63] finds a d-colouring with d = ̃O(n0.19747), building on.
Abstract. We show that approximate graph coloring is not solved by the lift.
Ciardo, Lorenzo; Živný, Stanislav (2025) Approximate Graph Coloring and the Crystal with a Hollow Shadow. SIAM Journal on Computing, 54 (4). doi:10.1137/24m1691594.
(PDF) Approximate Graph Colouring And The Hollow Shadow
ABSTRACT We show that approximate graph colouring is not solved by con-stantly many levels of the lift-and-project hierarchy for the com-bined basic linear programming and afine integer programming relaxation. The proof involves a construction of tensors whose fixed-dimensional projections are equal up to reflection and satisfy a sparsity condition, which may be of independent interest.
Ciardo, Lorenzo; Živný, Stanislav (2025) Approximate Graph Coloring and the Crystal with a Hollow Shadow. SIAM Journal on Computing, 54 (4). doi:10.1137/24m1691594.
Abstract. We show that approximate graph coloring is not solved by the lift.
We show that approximate graph colouring is not solved by constantly many levels of the lift-and-project hierarchy for the combined basic linear programming and affine integer programming relaxation. The proof involves a construction of tensors whose fixed-dimensional projections are equal up to reflection and satisfy a sparsity condition, which may be of independent interest.
Ciardo, Lorenzo; Živný, Stanislav (2025) Approximate Graph Coloring and the Crystal with a Hollow Shadow. SIAM Journal on Computing, 54 (4). doi:10.1137/24m1691594.
We show that approximate graph colouring is not solved by constantly many levels of the lift.
Among other things, we improve the state-of-the-art in approximate graph colouring by showing that, for any k ≥ 3, it is NP-hard to find a (2 k -1).
Export Conference item Approximate graph colouring and the hollow shadow Abstract: We show that approximate graph colouring is not solved by constantly many levels of the liftand.
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We show that approximate graph colouring is not solved by constantly many levels of the lift.
We show that approximate graph colouring is not solved by constantly many levels of the lift-and-project hierarchy for the combined basic linear programming and affine integer programming relaxation. The proof involves a construction of tensors whose fixed-dimensional projections are equal up to reflection and satisfy a sparsity condition, which may be of independent interest.
Approximate Graph Colouring and the Hollow Shadow.Lorenzo Ciardo, Stanislav Zivny (University of Oxford).
ABSTRACT We show that approximate graph colouring is not solved by con-stantly many levels of the lift-and-project hierarchy for the com-bined basic linear programming and afine integer programming relaxation. The proof involves a construction of tensors whose fixed-dimensional projections are equal up to reflection and satisfy a sparsity condition, which may be of independent interest.
The Hollow Crystal í µí° ¶, And Its Shadows. | Download Scientific Diagram
Among other things, we improve the state-of-the-art in approximate graph colouring by showing that, for any k ≥ 3, it is NP-hard to find a (2 k -1).
Approximate Graph Colouring and the Hollow Shadow.Lorenzo Ciardo, Stanislav Zivny (University of Oxford).
Abstract. We show that approximate graph coloring is not solved by the lift.
c-colourable graph, where 3 ≤ c ≤ d. There is a huge gap in our understanding of this problem. For an n-vertex graph and c = 3, the best known polynomial-time algorithm of Kawarabayashi, Thorup, and Yoneda [63] finds a d-colouring with d = ̃O(n0.19747), building on.
STOC 2023 - 4A - Approximate Graph Colouring And The Hollow Shadow ...
ABSTRACT We show that approximate graph colouring is not solved by con-stantly many levels of the lift-and-project hierarchy for the com-bined basic linear programming and afine integer programming relaxation. The proof involves a construction of tensors whose fixed-dimensional projections are equal up to reflection and satisfy a sparsity condition, which may be of independent interest.
We show that approximate graph colouring is not solved by constantly many levels of the lift-and-project hierarchy for the combined basic linear programming and affine integer programming relaxation. The proof involves a construction of tensors whose fixed-dimensional projections are equal up to reflection and satisfy a sparsity condition, which may be of independent interest.
c-colourable graph, where 3 ≤ c ≤ d. There is a huge gap in our understanding of this problem. For an n-vertex graph and c = 3, the best known polynomial-time algorithm of Kawarabayashi, Thorup, and Yoneda [63] finds a d-colouring with d = ̃O(n0.19747), building on.
Abstract. We show that approximate graph coloring is not solved by the lift.
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ABSTRACT We show that approximate graph colouring is not solved by con-stantly many levels of the lift-and-project hierarchy for the com-bined basic linear programming and afine integer programming relaxation. The proof involves a construction of tensors whose fixed-dimensional projections are equal up to reflection and satisfy a sparsity condition, which may be of independent interest.
Approximate Graph Colouring and the Hollow Shadow.Lorenzo Ciardo, Stanislav Zivny (University of Oxford).
Among other things, we improve the state-of-the-art in approximate graph colouring by showing that, for any k ≥ 3, it is NP-hard to find a (2 k -1).
Abstract. We show that approximate graph coloring is not solved by the lift.
Figure 1 From Approximate Graph Colouring And The Crystal With A Hollow ...
ABSTRACT We show that approximate graph colouring is not solved by con-stantly many levels of the lift-and-project hierarchy for the com-bined basic linear programming and afine integer programming relaxation. The proof involves a construction of tensors whose fixed-dimensional projections are equal up to reflection and satisfy a sparsity condition, which may be of independent interest.
We show that approximate graph colouring is not solved by constantly many levels of the lift.
Export Conference item Approximate graph colouring and the hollow shadow Abstract: We show that approximate graph colouring is not solved by constantly many levels of the liftand.
Among other things, we improve the state-of-the-art in approximate graph colouring by showing that, for any k ≥ 3, it is NP-hard to find a (2 k -1).
c-colourable graph, where 3 ≤ c ≤ d. There is a huge gap in our understanding of this problem. For an n-vertex graph and c = 3, the best known polynomial-time algorithm of Kawarabayashi, Thorup, and Yoneda [63] finds a d-colouring with d = ̃O(n0.19747), building on.
We show that approximate graph colouring is not solved by constantly many levels of the lift-and-project hierarchy for the combined basic linear programming and affine integer programming relaxation. The proof involves a construction of tensors whose fixed-dimensional projections are equal up to reflection and satisfy a sparsity condition, which may be of independent interest.
Export Conference item Approximate graph colouring and the hollow shadow Abstract: We show that approximate graph colouring is not solved by constantly many levels of the liftand.
We show that approximate graph colouring is not solved by constantly many levels of the lift.
Among other things, we improve the state-of-the-art in approximate graph colouring by showing that, for any k ≥ 3, it is NP-hard to find a (2 k -1).
Abstract. We show that approximate graph coloring is not solved by the lift.
ABSTRACT We show that approximate graph colouring is not solved by con-stantly many levels of the lift-and-project hierarchy for the com-bined basic linear programming and afine integer programming relaxation. The proof involves a construction of tensors whose fixed-dimensional projections are equal up to reflection and satisfy a sparsity condition, which may be of independent interest.
Approximate Graph Colouring and the Hollow Shadow.Lorenzo Ciardo, Stanislav Zivny (University of Oxford).
Ciardo, Lorenzo; Živný, Stanislav (2025) Approximate Graph Coloring and the Crystal with a Hollow Shadow. SIAM Journal on Computing, 54 (4). doi:10.1137/24m1691594.
