共查询到20条相似文献，搜索用时 15 毫秒
1.
Xuding Zhu 《Journal of Graph Theory》1999,30(1):1-6
We shall prove that for any graph H that is a core, if χ(G) is large enough, then H × G is uniquely H‐colorable. We also give a new construction of triangle free graphs, which are uniquely n‐colorable. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 1–6, 1999 相似文献
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《Journal of Graph Theory》2018,87(4):460-474
An odd k‐edge‐coloring of a graph G is a (not necessarily proper) edge‐coloring with at most k colors such that each nonempty color class induces a graph in which every vertex is of odd degree. Pyber (1991) showed that every simple graph is odd 4‐edge‐colorable, and Lužar et al. (2015) showed that connected loopless graphs are odd 5‐edge‐colorable, with one particular exception that is odd 6‐edge‐colorable. In this article, we prove that connected loopless graphs are odd 4‐edge‐colorable, with two particular exceptions that are respectively odd 5‐ and odd 6‐edge‐colorable. Moreover, a color class can be reduced to a size at most 2. 相似文献
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A snark is a cubic cyclically 4–edge connected graph with edge chromatic number four and girth at least five. We say that a graph G is odd 2–factored if for each 2–factor F of G each cycle of F is odd. In this extended abstract, we present a method for constructing odd 2–factored snarks. In particular, we construct two families of odd 2–factored snarks of order 26 and 34 that disprove a previous conjecture by some of the authors. 相似文献
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David Défossez 《Journal of Graph Theory》2009,62(2):139-156
In this paper we investigate the problem of clique‐coloring, which consists in coloring the vertices of a graph in such a way that no monochromatic maximal clique appears, and we focus on odd‐hole‐free graphs. On the one hand we do not know any odd‐hole‐free graph that is not 3‐clique‐colorable, but on the other hand it is NP‐hard to decide if they are 2‐clique‐colorable, and we do not know if there exists any bound k0 such that they are all k0 ‐clique‐colorable. First we will prove that (odd hole, codiamond)‐free graphs are 2‐clique‐colorable. Then we will demonstrate that the complexity of 2‐clique‐coloring odd‐hole‐free graphs is actually Σ2 P‐complete. Finally we will study the complexity of deciding whether or not a graph and all its subgraphs are 2‐clique‐colorable. © 2009 Wiley Periodicals, Inc. J Graph Theory 62: 139–156, 2009 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f(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为奇优美图,f称为G的奇优美标号.设G=〈V,E〉是一个无向简单图.如果存在一个映射f:V(G)→{0,1,2,…,2|E|-1},满足:1)f是单射;2)■uv∈E(G),令f(uv)=f(u)+f(v),有{f(uv)|uv∈E(G)}={1,3,5,…,2|E|-1},则称G是奇强协调图,f称为G的.奇强协调标号或奇强协调值.给出了链图、升降梯等几类有趣图的奇优美标号和奇强协调标号. 相似文献
7.
Joseph Barback 《Mathematical Logic Quarterly》2006,52(4):359-361
In this paper we present a contribution to a classical result of E. Ellentuck in the theory of regressive isols. E. Ellentuck introduced the concept of a hyper‐torre isol, established their existence for regressive isols, and then proved that associated with these isols a special kind of semi‐ring of isols is a model of the true universal‐recursive statements of arithmetic. This result took on an added significance when it was later shown that for regressive isols, the property of being hyper‐torre is equivalent to being hereditarily odd‐even. In this paper we present a simplification to the original proof for establishing that equivalence. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Christian Löwenstein Anders Sune Pedersen Dieter Rautenbach Friedrich Regen 《Journal of Graph Theory》2011,67(2):96-111
We prove several tight lower bounds in terms of the order and the average degree for the independence number of graphs that are connected and/or satisfy some odd girth condition. Our main result is the extension of a lower bound for the independence number of triangle‐free graphs of maximum degree at most three due to Heckman and Thomas [Discrete Math 233 (2001), 233–237] to arbitrary triangle‐free graphs. For connected triangle‐free graphs of order n and size m, our result implies the existence of an independent set of order at least (4n?m?1)/7. © 2010 Wiley Periodicals, Inc. J Graph Theory 67:96‐111, 2011 相似文献
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David Dfossez 《Journal of Graph Theory》2006,53(3):233-249
We consider the problem of clique‐coloring, that is coloring the vertices of a given graph such that no maximal clique of size at least 2 is monocolored. Whereas we do not know any odd‐hole‐free graph that is not 3‐clique‐colorable, the existence of a constant C such that any perfect graph is C‐clique‐colorable is an open problem. In this paper we solve this problem for some subclasses of odd‐hole‐free graphs: those that are diamond‐free and those that are bull‐free. We also prove the NP‐completeness of 2‐clique‐coloring K4‐free perfect graphs. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 233–249, 2006 相似文献
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In the setting of ZF, i.e., Zermelo–Fraenkel set theory without the Axiom of Choice (AC), we study partitions of Russell‐sets into sets each with exactly n elements (called n ‐ary partitions), for some integer n. We show that if n is odd, then a Russell‐set X has an n ‐ary partition if and only if |X | is divisible by n. Furthermore, we establish that it is relative consistent with ZF that there exists a Russell‐set X such that |X | is not divisible by any finite cardinal n > 1 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Under what conditions is it true that if there is a graph homomorphism G □ H → G □ T, then there is a graph homomorphism H→ T? Let G be a connected graph of odd girth 2k + 1. We say that G is (2k + 1)‐angulated if every two vertices of G are joined by a path each of whose edges lies on some (2k + 1)‐cycle. We call G strongly (2k + 1)‐angulated if every two vertices are connected by a sequence of (2k + 1)‐cycles with consecutive cycles sharing at least one edge. We prove that if G is strongly (2k + 1)‐angulated, H is any graph, S, T are graphs with odd girth at least 2k + 1, and ?: G□ H→S□T is a graph homomorphism, then either ? maps G□{h} to S□{th} for all h∈V(H) where th∈V(T) depends on h; or ? maps G□{h} to {sh}□ T for all h∈V(H) where sh∈V(S) depends on h. This theorem allows us to prove several sufficient conditions for a cancelation law of a graph homomorphism between two box products with a common factor. We conclude the article with some open questions. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:221‐238, 2008 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(5):1743-1752
The good Boussinesq equation is endowed with symplectic conservation law and energy conservation law. In this paper, some new highly efficient structure‐preserving methods for the good Boussinesq equation are proposed by improving the standard finite difference method (FDM). The new methods only use and calculate values at the odd (or even) nodes to reduce the computational cost. We call this kind of methods odd‐even method (OEM). Numerical results show that the OEM and the standard FDM have nearly the same numerical errors under the same mesh partition. However, the OEM is much more efficient than the standard FDM, such as the consumed CPU time and occupied memory. 相似文献
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对简单图G=〈V,E〉,如果存在一个映射f:V→{0,1,2,…,2 E-1}满足1)对任意的u,v∈V,若u≠v,则f(u)≠f(v);2)对任意的e1,e2∈E,若e1≠e2,则g(e1)≠g(e2),此处g(e)=f(u)+f(v),e=uv;3){g(e)e∈E}={1,3,5,…,2 E-1},则称G为奇强协调图,f称为G的奇强协调标号.给出了直径为4的树的奇强协调标号. 相似文献
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Tom Bohman 《Proceedings of the American Mathematical Society》2003,131(11):3559-3569
This paper contains a construction for independent sets in the powers of odd cycles. It follows from this construction that the limit as goes to infinity of is zero, where is the Shannon capacity of the graph .
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Tom Bohman 《Proceedings of the American Mathematical Society》2005,133(2):537-543
It follows from a construction for independent sets in the powers of odd cycles given in the predecessor of this paper that the limit as goes to infinity of is zero, where is the Shannon capacity of a graph . This paper contains a shorter proof of this limit theorem that is based on an `expansion process' introduced in an older paper of L. Baumert, R. McEliece, E. Rodemich, H. Rumsey, R. Stanley and H. Taylor. We also refute a conjecture from that paper, using ideas from the predecessor of this paper.
17.
A. Nilli 《Journal of Graph Theory》1999,31(2):145-147
It is shown that any 4‐chromatic graph on n vertices contains an odd cycle of length smaller than √8n. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 145–147, 1999 相似文献
18.
Tams Mtrai 《Journal of Graph Theory》2006,53(1):77-82
We prove that any finite simple graph can be covered by three of its odd subgraphs, and we construct an infinite sequence of graphs where an edge‐disjoint covering by three odd subgraphs is not possible. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 77–82, 2006 相似文献
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ZHANG ShiQing 《中国科学 数学(英文版)》2012,(4):719-723
Using variational minimizing methods,we prove the existence of the odd symmetric parabolic or hyperbolic orbit for the restricted 3-body problems with weak forces. 相似文献
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Pace P. Nielsen. 《Mathematics of Computation》2007,76(260):2109-2126
An odd perfect number, , is shown to have at least nine distinct prime factors. If then must have at least twelve distinct prime divisors. The proof ultimately avoids previous computational results for odd perfect numbers.