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一个图G 的无圈k- 边染色是指G 的一个正常的不产生双色圈的k- 边染色. G 的无圈边色数a′(G) 定义为使得G 有一个无圈k- 边染色的最小的整数k. 本文完全刻画了最大度不为4 的没有K4-图子式的图的无圈边色数. 相似文献
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对于一个图G的正常边着色,如果此种边着色使得该图没有2—色的圈,那么这种边着色被称为是G的无圈边着色.用d(G)表示图G的无圈边色数,即G的无圈边着色中所使用的最小颜色数.Alon N,Sadakov B and Zaks A在[1]中有如下结果:对于围长至少是2000△(G)log△(G)的图G,有d(G)≤△ 2,其中△是图G的最大度.我们改进了这个结果,得到了如下结论:对于围长至少是700△(G)log△(G)的图G,有d(G)≤△ 2. 相似文献
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A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G, denoted by χ a(G), is the least number of colors such that G has an acyclic edge coloring. A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that χ a(G) ≤Δ(G) + 22, if G is a triangle-free 1-planar graph. 相似文献
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An acyclic edge coloring of a graph G is a proper edge coloring such that there are no bichromatic cycles.The acyclic edge chromatic number of a graph G is the minimum number k such that there exists an acyclic edge coloring using k colors and is denoted by χ’ a(G).In this paper we prove that χ ’ a(G) ≤(G) + 5 for planar graphs G without adjacent triangles. 相似文献
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Lin SUN 《数学学报(英文版)》2021,(6):992-1004
A proper vertex coloring of a graph is acyclic if every cycle uses at least three colors. A graph G is acyclically k-choosable if for any list assignment L = {L(v) : v ∈ V(G)} with |L(v)| ≥ k for all v ∈ V(G), there exists a proper acyclic vertex coloring φ of G such that φ(v) ∈ L(v) for all v ∈ V(G). In this paper, we prove that if G is a planar graph and contains no 5-cycles and no adjacent 4-cycles, then G is acyclically 6-choosable. 相似文献
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An acyclic colouring of a graph G is a proper vertex colouring such that every cycle uses at least three colours. For a list assignment L = {L(v)| v∈V(G)}, if there exists an acyclic colouringρ such that ρ(v)∈L(v) for each v∈V(G), then ρ is called an acyclic L-list colouring of G. If there exists an acyclic L-list colouring of G for any L with |L(v)|≥k for each v∈V(G), then G is called acyclically k-choosable. In this paper, we prove that every graph with maximum degree Δ≤7 is acyclically 13-cho... 相似文献
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We prove the theorem from the title: the acyclic edge chromatic number of a random d‐regular graph is asymptotically almost surely equal to d + 1. This improves a result of Alon, Sudakov, and Zaks and presents further support for a conjecture that Δ(G) + 2 is the bound for the acyclic edge chromatic number of any graph G. It also represents an analog of a result of Robinson and the second author on edge chromatic number. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 69–74, 2005 相似文献
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Yoav Segev 《Israel Journal of Mathematics》1993,82(1-3):381-394
In this paper we develop some homological techniques to obtain fixed points for groups acting on finite Z-acyclic complexes.
In particular we show that if a groupG acts on a finite 2-dimensional acyclic simplicial complexD, then the fixed point set ofG onD is either empty or acyclic. We supply some machinery for determining which of the two cases occurs. The Feit-Thompson Odd
Order Theorem is used in obtaining this result.
This paper is dedicated to Prof. John G. Thompson on the occasion of receiving the Wolf Prize, 1992
This work was partially supported by BSF 88-00164. 相似文献
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For graphs of bounded maximum degree, we consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges between two colour classes is acyclic, and each colour class induces a graph with maximum degree at most t.We consider the supremum, over all graphs of maximum degree at most d, of the acyclic t-improper chromatic number and provide t-improper analogues of results by Alon, McDiarmid and Reed [N. Alon, C.J.H. McDiarmid, B. Reed, Acyclic coloring of graphs, Random Structures Algorithms 2 (3) (1991) 277-288] and Fertin, Raspaud and Reed [G. Fertin, A. Raspaud, B. Reed, Star coloring of graphs, J. Graph Theory 47 (3) (2004) 163-182]. 相似文献
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G. Dupont 《Journal of Pure and Applied Algebra》2011,215(4):628-641
Let Q be an acyclic quiver. We introduce the notion of generic variables for the coefficient-free acyclic cluster algebra A(Q). We prove that the set G(Q) of generic variables contains naturally the set M(Q) of cluster monomials in A(Q) and that these two sets coincide if and only if Q is a Dynkin quiver. We establish multiplicative properties of these generic variables analogous to multiplicative properties of Lusztig’s dual semicanonical basis. This allows to compute explicitly the generic variables when Q is a quiver of affine type. When Q is the Kronecker quiver, the set G(Q) is a Z-basis of A(Q) and this basis is compared to Sherman-Zelevinsky and Caldero-Zelevinsky bases. 相似文献
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本文研究有向图的全有效控制集.通过对无圈有向图结构特征的刻画,给出了简单图G在定向D下有全有效控制集的充要条件,并对几类特殊图的全有效数进行了计算. 相似文献
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A natural digraph analog of the graph theoretic concept of “an independent set” is that of “an acyclic set of vertices,” namely a set not spanning a directed cycle. By this token, an analog of the notion of coloring of a graph is that of decomposition of a digraph into acyclic sets. We extend some known results on independent sets and colorings in graphs to acyclic sets and acyclic colorings of digraphs. In particular, we prove bounds on the topological connectivity of the complex of acyclic sets, and using them we prove sufficient conditions for the existence of acyclic systems of representatives of a system of sets of vertices. These bounds generalize a result of Tardos and Szabó. We prove a fractional version of a strong‐acyclic‐coloring conjecture for digraphs. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 177–189, 2008 相似文献
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Matthew B Squire 《Journal of Algorithms in Cognition, Informatics and Logic》1998,26(2):275-290
The acyclic orientations of a graph are related to its chromatic polynomial, to its reliability, and to certain hyperplane arrangements. In this paper, an algorithm for listing the acyclic orientations of a graph is presented. The algorithm is shown to requireO(n) time per acyclic orientation generated. This is the most efficient algorithm known for generating acyclic orientations. 相似文献
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A signed graph is a graph whose edges are labelled positive or negative. A signed graph is said to be balanced if the set of negative edges form a cut. The balanced induced subgraph polytopeP(G) of a graphG is the convex hull of the incidence vectors of all node sets that induce balanced subgraphs ofG. In this paper we exhibit various (rank) facet defining inequalities. We describe several methods with which new facet defining inequalities ofP(G) can be constructed from known ones. Finding a maximum weighted balanced induced subgraph of a series parallel graph is a polynomial problem. We show that for this class of graphsP(G) may have complicated facet defining inequalities. We derive analogous results for the polytope of acyclic induced subgraphs.Research supported in part by the Natural Sciences and Engineering Research Council of Canada; the second author has also been supported by C.P. Rail. 相似文献
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A k-colouring(not necessarily proper) of vertices of a graph is called acyclic, if for every pair of distinct colours i and j the subgraph induced by the edges whose endpoints have colours i and j is acyclic. We consider acyclic k-colourings such that each colour class induces a graph with a given(hereditary) property. In particular, we consider acyclic k-colourings in which each colour class induces a graph with maximum degree at most t, which are referred to as acyclic t-improper k-colourings. The acyclic t-improper chromatic number of a graph G is the smallest k for which there exists an acyclic t-improper k-colouring of G. We focus on acyclic colourings of graphs with maximum degree 4. We prove that 3 is an upper bound for the acyclic 3-improper chromatic number of this class of graphs. We also provide a non-trivial family of graphs with maximum degree4 whose acyclic 3-improper chromatic number is at most 2, namely, the graphs with maximum average degree at most 3. Finally, we prove that any graph G with Δ(G) 4 can be acyclically coloured with 4 colours in such a way that each colour class induces an acyclic graph with maximum degree at most 3. 相似文献