List H-Coloring a Graph by Removing Few Vertices
List H-Coloring a Graph by Removing Few Vertices
复制标题
通过删除少量顶点对图进行列表 H 着色
DOI：
10.1007/s00453-016-0139-6
复制
发表时间：
2013
期刊：
影响因子：
1.1
通讯作者：
D. Marx
中科院分区：
文献类型：
--
作者：
R. Chitnis;László Egri;D. Marx
在列表同构问题的删除版本中，我们得到了Gragrs g和h，列表l（v）⊆（h）\ documentClass [12pt] {minimal} \ usepackage {amsmath} \ usepackage {wasysym} AMSFONTS} \ USEPACKAGE {AMSSYMB} \ USEPACKAGE {AMSBSY} \ USEPACKAGE {MATHRSFS} \ usePackage {upgreek} \ setLength每个顶点v∈V（g）\ documentClass [12pt] {minimal} \ usepackage {amsmath} \ usepackage {wasySym} \ usepackage {amsfonts {amsfonts} {Mathrsfs} \ usepackage {upgreek} \ setLength {\ oddSidemargin} { - 69pt} \ begin {document {document} $$ v \ in v（g）$$ \ end End \ end \ end \ end \ end \ end \ end document {document}和integer k and integer k。 W⊆V(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \ usepackage{upgreek} \ setLength {\ oddsIdeMargin} { - 69pt} \ begin {document} $$ w \ subseteq v（g）$$ $ end \ end \ end \ end {document {document} size of k size toss k y toss k y toss k in Doss的大小，因此来自G \ w \ documentClass [12pt formandclass [12pt] {minimal} \ usepackage {amsmath} \ usepackage {wasysym} \ usepackage {amsfonts} \ usepackage {amssymb} \ usepackage {amssymb} {-69PT} \ BEGIN {document} $$ g {\ setMinus} w $$ \ end {document {document} hor尊重列表。 \ use-package {amsfonts} \ usepackage {amssymb} \ usepackage {amsbsy} \ usepackage {mathrsfs} \ usepackage {usepackage {upgreek} \ upgreek} \ setLength由k和| h |参数化的document}）是可用于任何（P6，c6）\ documentClass [12pt] {minimal} \ usepackage {amsmath} \ usepackage {wasySym} amssymb} \ usepackage {amsbsy} \ usepackage {mathrsfs} \ usepackage { h；对于此限制的图表，该问题概括了顶点覆盖，奇数循环和顶点多路被切割的大小和终端的数量。 {minimal} \ usepackage {amsmath} \ usepackage {wasysym} \ usepackage {amsfonts} \ usepackage {amssymb} \ usepackage {amssymb} {-69PT} \ BEGIN {document} $$ {h} $$ \ end {document {document}）是固定参数，可用于列表同构问题（无删除）的图形h。 。一个相当自然的满意度问题，条款删除链条。
In the deletion version of the list homomorphism problem, we are given graphs G and H, a list L(v)⊆V(H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L(v)\subseteq V(H)$$\end{document} for each vertex v∈V(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v\in V(G)$$\end{document}, and an integer k. The task is to decide whether there exists a set W⊆V(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W \subseteq V(G)$$\end{document} of size at most k such that there is a homomorphism from G\W\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G {\setminus } W$$\end{document} to H respecting the lists. We show that DL-Hom(H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}$$\end{document}), parameterized by k and |H|, is fixed-parameter tractable for any (P6,C6)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(P_6,C_6)$$\end{document}-free bipartite graph H; already for this restricted class of graphs, the problem generalizes Vertex Cover, Odd Cycle Transversal, and Vertex Multiway Cut parameterized by the size of the cutset and the number of terminals. We conjecture that DL-Hom(H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}$$\end{document}) is fixed-parameter tractable for the class of graphs H for which the list homomorphism problem (without deletions) is polynomial-time solvable; by a result of Feder et al. (Combinatorica 19(4):487–505, 1999), a graph H belongs to this class precisely if it is a bipartite graph whose complement is a circular arc graph. We show that this conjecture is equivalent to the fixed-parameter tractability of a single fairly natural satisfiability problem, Clause Deletion Chain-SAT.
影响因子：
0.5
作者：
Egri L
通讯作者：
Egri L