NP-Hardness of Almost Coloring Almost 3-Colorable Graphs

IF 0.7 4区物理与天体物理 Q4 PHYSICS, APPLIED Spin Pub Date : 2023-01-01 DOI:10.4230/LIPIcs.APPROX/RANDOM.2023.51

Yahli Hecht, Dor Minzer, S. Safra

引用次数: 1

Abstract

A graph G = ( V, E ) is said to be ( k, δ ) almost colorable if there is a subset of vertices V ′ ⊆ V of size at least (1 − δ ) | V | such that the induced subgraph of G on V ′ is k -colorable. We prove that for all k , there exists δ > 0 such for all ε > 0, given a graph G it is NP-hard (under randomized reductions) to distinguish between:

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概着色概3色图的np -硬度

如果存在一个大小至少为(1−δ) | V |的顶点V '的子集，使得G在V '上的诱导子图是k可色的，则图G = (V, E)是(k， δ)几乎可色的。我们证明了对于所有k，存在δ > 0，使得对于所有ε > 0，给定一个图G，它是np困难的(在随机化简下)来区分:

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Spin Materials Science-Electronic, Optical and Magnetic Materials

CiteScore

2.10

自引率

11.10%

发文量

期刊介绍： Spin electronics encompasses a multidisciplinary research effort involving magnetism, semiconductor electronics, materials science, chemistry and biology. SPIN aims to provide a forum for the presentation of research and review articles of interest to all researchers in the field. The scope of the journal includes (but is not necessarily limited to) the following topics: *Materials: -Metals -Heusler compounds -Complex oxides: antiferromagnetic, ferromagnetic -Dilute magnetic semiconductors -Dilute magnetic oxides -High performance and emerging magnetic materials *Semiconductor electronics *Nanodevices: -Fabrication -Characterization *Spin injection *Spin transport *Spin transfer torque *Spin torque oscillators *Electrical control of magnetic properties *Organic spintronics *Optical phenomena and optoelectronic spin manipulation *Applications and devices: -Novel memories and logic devices -Lab-on-a-chip -Others *Fundamental and interdisciplinary studies: -Spin in low dimensional system -Spin in medical sciences -Spin in other fields -Computational materials discovery