共查询到20条相似文献,搜索用时 46 毫秒
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《Quaestiones Mathematicae》2013,36(2):259-264
AbstractAn F-free colouring of a graph G is a partition {V1,V2,…,Vn} of the vertex set V(G) of G such that F is not an induced subgraph of G[Vi] for each i. A graph is uniquely F-free colourable if any two .F-free colourings induce the same partition of V(G). We give a constructive proof that uniquely C4-free colourable graphs exist. 相似文献
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WANGWEIFAN ZHANGKEMIN 《高校应用数学学报(英文版)》1997,12(4):455-462
A Planar graph g is called a ipseudo outerplanar graph if there is a subset v.∈V(G),[V.]=i,such that G-V. is an outerplanar graph in particular when G-V.is a forest ,g is called a i-pseudo-tree .in this paper.the following results are proved;(1)the conjecture on the total coloring is true for all 1-pseudo-outerplanar graphs;(2)X1(G) 1 fo any 1-pseudo outerplanar graph g with △(G)≥3,where x4(G)is the total chromatic number of a graph g. 相似文献
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A graph with nodes 1, …, n is a threshold signed graph if one can find two positive real numbers S, T and real numbers a1, …, an associated with the vertices in such a way that i, j are linked iff either |ai + aj| ≥ S or |ai - aj| ≥ T. Such graphs generalize threshold graphs. It is shown that these graphs are precisely the graphs with Dilworth number at most two (the Dilworth number is the maximum number of pairwise incomparable vertices in the vicinal preorder). Some other properties of this subclass of perfect graphs are also presented. The graphs considered in this paper are finite simple graphs G = (V, E), where V is the vertex set of G and E a subset of pairs of G. For x V, N(x) denotes the neighbor set of x: N(x) = {y | {x, y} E}. 相似文献
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徐新萍 《数学的实践与认识》2009,39(10)
设G是一个图,G的部分平方图G*满足V(G*)=V(G),E(G*)=E(G)∪{uv:uv■E(G),且J(u,v)≠■},这里J(u,v)={w∈N(u)∩N(v):N(w)■N[u]∪N[v]}.利用插点方法,证明了如下结果:设G是k-连通图(k2),b是整数,0min {k,(2b-1+k)/2}(n(Y)-1),则G是哈密尔顿图.同时给出图是1-哈密尔顿的和哈密尔顿连通的相关结果. 相似文献
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Yuan Jinjiang 《Journal of Graph Theory》1998,28(4):203-213
We say that a simple graph G is induced matching extendable, shortly IM-extendable, if every induced matching of G is included in a perfect matching of G. The main results of this paper are as follows: (1) For every connected IM-extendable graph G with |V(G)| ≥ 4, the girth g(G) ≤ 4. (2) If G is a connected IM-extendable graph, then |E(G)| ≥ ${3\over 2}|V(G)| - 2$; the equality holds if and only if G ≅ T × K2, where T is a tree. (3) The only 3-regular connected IM-extendable graphs are Cn × K2, for n ≥ 3, and C2n(1, n), for n ≥ 2, where C2n(1, n) is the graph with 2n vertices x0, x1, …, x2n−1, such that xixj is an edge of C2n(1, n) if either |i − j| ≡ 1 (mod 2n) or |i − j| ≡ n (mod 2n). © 1998 John Wiley & Sons, Inc. J. Graph Theory 28: 203–213, 1998 相似文献
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《Quaestiones Mathematicae》2013,36(4):383-398
Abstract A set B of vertices of a graph G = (V,E) is a k-maximal independent set (kMIS) if B is independent but for all ?-subsets X of B, where ? ? k—1, and all (? + 1)-subsets Y of V—B, the set (B—X) u Y is dependent. A set S of vertices of C is a k-maximal clique (kMc) of G iff S is a kMIS of [Gbar]. Let βk, (G) (wk(G) respectively) denote the smallest cardinality of a kMIS (kMC) of G—obviously βk(G) = wk([Gbar]). For the sequence m1 ? m2 ?…? mn = r of positive integers, necessary and sufficient conditions are found for a graph G to exist such that wk(G) = mk for k = 1,2,…,n and w(G) = r (equivalently, βk(G) = mk for k = 1,2,…,n and β(G) = r). Define sk(?,m) to be the largest integer such that for every graph G with at most sk(?,m) vertices, βk(G) ? ? or wk(G) ? m. Exact values for sk(?,m) if k ≥ 2 and upper and lower bounds for s1(?,m) are de termined. 相似文献
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A decomposition ??={G1, G2,…,Gs} of a graph G is a partition of the edge set of G into edge‐disjoint subgraphs G1, G2,…,Gs. If Gi?H for all i∈{1, 2, …, s}, then ?? is a decomposition of G by H. Two decompositions ??={G1, G2, …, Gn} and ?={F1, F2,…,Fn} of the complete bipartite graph Kn,n are orthogonal if |E(Gi)∩E(Fj)|=1 for all i,j∈{1, 2, …, n}. A set of decompositions {??1, ??2, …, ??k} of Kn, n is a set of k mutually orthogonal graph squares (MOGS) if ??i and ??j are orthogonal for all i, j∈{1, 2, …, k} and i≠j. For any bipartite graph G with n edges, N(n, G) denotes the maximum number k in a largest possible set {??1, ??2, …, ??k} of MOGS of Kn, n by G. El‐Shanawany conjectured that if p is a prime number, then N(p, Pp+ 1)=p, where Pp+ 1 is the path on p+ 1 vertices. In this article, we prove this conjecture. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 369–373, 2009 相似文献
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《Discrete Mathematics》1986,58(1):63-78
In this paper we give a procedure by which Hamiltonian decompositions of the s-partite graph Kn,n,…,n, where (s − 1)n is even, can be constructed. For 2t⩽s, 1⩽a1⩽…⩽at⩽n, we find conditions which are necessary and sufficient for a decomposition of the edge-set of Ka1a2…,at into (s − 1)n/2 classes, each class consisting of disjoint paths, to be extendible to a Hamiltonian decomposition of the complete s-partite graph Krmn,n,…,n so that each of the classes forms part of a Hamiltonian cycle. 相似文献
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A graph G is called an (n,k)-graph if κ(G-S)=n-|S| for any S ? V(G) with |S| ≤ k, where ?(G) denotes the connectivity of G. Mader conjectured that for k ≥ 3 the graph K2k+2?(1-factor) is the unique (2k, k)-graph. Kriesell has settled two special cases for k = 3,4. We prove the conjecture for the general case k ≥ 5. 相似文献
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对于简单图G=〈V,E〉,如果存在一个映射f:V(G)→{0,1,2,…,2 |E|-1}满足1)对任意的u,v∈V,若u≠v,则(u)≠f(v);2)max{f(v)|v∈V}=2|E|-1;3)对任意的e_1,e_2∈E,若e_1≠e_2,则g(e_1)≠g(e_2),此处g(e)=|f(u)+f(v)|,e=uv;4){g(e)|e∈E}={1,3,5,…,2|E|-1},则称G是奇优美图,f称为G的奇优美标号.Gnanajoethi提出了一个猜想:每棵树都是奇优美的.证明了图P_(r,(2s-1)是奇优美图. 相似文献
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Jarmila Chvátalová 《Discrete Mathematics》1975,11(3):249-253
If G is a graph with p vertices and at least one edge, we set φ (G) = m n max |f(u) ? f(v)|, where the maximum is taken over all edges uv and the minimum over all one-to-one mappings f : V(G) → {1, 2, …, p}: V(G) denotes the set of vertices of G.Pn will denote a path of length n whose vertices are integers 1, 2, …, n with i adjacent to j if and only if |i ? j| = 1. Pm × Pn will denote a graph whose vertices are elements of {1, 2, …, m} × {1, 2, …, n} and in which (i, j), (r, s) are adjacent whenever either i = r and |j ? s| = 1 or j = s and |i ? r| = 1.Theorem.If max(m, n) ? 2, thenφ(Pm × Pn) = min(m, n). 相似文献
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Hong Wang 《Journal of Graph Theory》1999,31(2):101-106
In this article, we consider the following problem: Given a bipartite graph G and a positive integer k, when does G have a 2‐factor with exactly k components? We will prove that if G = (V1, V2, E) is a bipartite graph with |V1| = |V2| = n ≥ 2k + 1 and δ (G) ≥ ⌈n/2⌉ + 1, then G contains a 2‐factor with exactly k components. We conjecture that if G = (V1, V2; E) is a bipartite graph such that |V1| = |V2| = n ≥ 2 and δ (G) ≥ ⌈n/2⌉ + 1, then, for any bipartite graph H = (U1, U2; F) with |U1| ≤ n, |U2| ≤ n and Δ (H) ≤ 2, G contains a subgraph isomorphic to H. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 101–106, 1999 相似文献
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Stephen G. Penrice 《Journal of Graph Theory》1997,25(2):101-105
Motivated by earlier work on dominating cliques, we show that if a graph G is connected and contains no induced subgraph isomorphic to P6 or Ht (the graph obtained by subdividing each edge of K1,t, t ≥ 3, by exactly one vertex), then G has a dominating set which induces a connected graph with clique covering number at most t − 1. © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 101–105, 1997 相似文献
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Let k≥1 be an integer and G=(V 1,V 2;E) a bipartite graph with |V 1|=|V 2|=n such that n≥2k+2. Our result is as follows: If $d(x)+d(y)\geq \lceil\frac{4n+k}{3}\rceil$ for any nonadjacent vertices x∈V 1 and y∈V 2, then for any k distinct vertices z 1,…,z k , G contains a 2-factor with k+1 cycles C 1,…,C k+1 such that z i ∈V(C i ) and l(C i )=4 for each i∈{1,…,k}. 相似文献
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得到了对于二部图G=(V_1,V_2;E),当|V_1|=|V_2|=n≥2k+1时的结果:对G中任意2k条独立边e_1,e_1~*,…,e_k,e_k~*,G中一定存在k个独立的4-圈C_1,C_2,…,C_k,使得对任意i∈{1,2,…,k}有{e_i,e_i~*}E(C_i).并在此基础上进一步证明了当|V_1|=|V_2|=n≥3k时若对任意两顶点x∈V_1,y∈V_2,都有d(x)+d(y)≥2n-k+1成立,则G有一个2-因子含有k+1个独立圈C_1,C_2,…,C_(k+1)使得对任意i∈{1,2,…,k}有{e_i,e_i~*}E(C_i)且|C_i|=4. 相似文献
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Lü Changhong 《高校应用数学学报(英文版)》2007,22(1):1-6
A labeled graph is an ordered pair (G, L) consisting of a graph G and its labeling L : V(G) → {1,2 ,n}, where n = |V(G)|. An increasing nonconsecutive path in a labeled graph (G,L) is either a path (u1,u2 uk) (k ≥ 2) in G such that L(u,) + 2 ≤ L(ui+1) for all i = 1, 2, ..., k- 1 or a path of order 1. The total number of increasing nonconsecutive paths in (G, L) is denoted by d(G, L). A labeling L is optimal if the labeling L produces the largest d(G, L). In this paper, a method simpler than that in Zverovich (2004) to obtain the optimal labeling of path is given. The optimal labeling of other special graphs such as cycles and stars is obtained. 相似文献
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Let G be a graph of order n. We show that if G is a 2-connected graph and max{d(u), d(v)} + |N(u) U N(v)| ≥ n for each pair of vertices u, v at distance two, then either G is hamiltonian or G ?3Kn/3 U T1 U T2, where n ? O (mod 3), and T1 and T2 are the edge sets of two vertex disjoint triangles containing exactly one vertex from each Kn/3. This result generalizes both Fan's and Lindquester's results as well as several others. 相似文献