scholarly journals On the maximum number of odd cycles in graphs without smaller odd cycles

2021 ◽  
Author(s):  
Andrzej Grzesik ◽  
Bartłomiej Kielak
Keyword(s):  
Odd Cycles

Solar-cycle phenomena in cosmic-ray intensity: Differences between even and odd cycles

1988 ◽  
Vol 42 (3) ◽  
pp. 233-244 ◽  
Author(s):  
H. Mavromichalaki ◽  
E. Marmatsouri ◽  
A. Vassilaki
Keyword(s):  
Solar Cycle ◽  
Cosmic Ray ◽  
Cosmic Ray Intensity ◽  
Odd Cycles

Variations in solar and geomagnetic activity with periods near to 1.3 year

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Jaroslav Střeštïk
Keyword(s):  
Geomagnetic Activity ◽  
Time Series Data ◽  
Interplanetary Space ◽  
Short Interval ◽  
Biological Data ◽  
Series Data ◽  
Solar Cycles ◽  
Lower Amplitude ◽  
Periodic Signals ◽  
Odd Cycles

AbstractIt is known that solar wind velocity fluctuates regularly with a period of about 1.3 years. This periodicity (and other signals with periods near to 1.1 and 0.9 years) has also been observed in biological data. The variation is a temporary feature, mostly being observed in the early 1990s. Here, the occurrence of these periodic signals in solar and geomagnetic activity between 1932 and 2005 has been investigated. The signal with 1.3 year period is present in geomagnetic activity only in a short interval after 1990 and to a lesser extent around 1942. At other times the signal is very weak or not present at all. Other periods are much lower amplitude and appear only sporadically throughout the time investigated. A connection between these periods and solar cycles (e.g. different even or odd cycles) has not been proven. It is possible that there is a long-term periodicity in the occurrence of the 1.3 year period but the time series data available is insufficient to confirm this. There are no such periodicities in solar activity. In order to gain a greater understanding of these periodic signals, we should search for their origin in interplanetary space.

scholarly journals Between 2- and 3-Colorability

10.37236/4673 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Alan Frieze ◽  
Wesley Pegden
Keyword(s):  
Positive Integer ◽  
Random Graphs ◽  
The Other ◽  
Chromatic Numbers ◽  
Other Hand ◽  
Odd Cycles

We consider the question of the existence of homomorphisms between $G_{n,p}$ and odd cycles when $p=c/n$, $1<c\leq 4$. We show that for any positive integer $\ell$, there exists $\epsilon=\epsilon(\ell)$ such that if $c=1+\epsilon$ then w.h.p. $G_{n,p}$ has a homomorphism from $G_{n,p}$ to $C_{2\ell+1}$ so long as its odd-girth is at least $2\ell+1$. On the other hand, we show that if $c=4$ then w.h.p. there is no homomorphism from $G_{n,p}$ to $C_5$. Note that in our range of interest, $\chi(G_{n,p})=3$ w.h.p., implying that there is a homomorphism from $G_{n,p}$ to $C_3$.  These results imply the existence of random graphs with circular chromatic numbers $\chi_c$ satisfying $2<\chi_c(G)<2+\delta$ for arbitrarily small $\delta$, and also that $2.5\leq \chi_c(G_{n,\frac 4 n})<3$ w.h.p.

scholarly journals A note on compact and compact circular edge-colorings of graphs

2008 ◽  
Vol Vol. 10 no. 3 (Graph and Algorithms) ◽  
Author(s):  
Dariusz Dereniowski ◽  
Adam Nadolski
Keyword(s):  
Approximation Algorithm ◽  
Decision Problem ◽  
Edge Coloring ◽  
Exact Algorithm ◽  
Weighted Graphs ◽  
Edge Colorings ◽  
Odd Cycle ◽  
International Audience ◽  
Np Complete ◽  
Odd Cycles

Graphs and Algorithms International audience We study two variants of edge-coloring of edge-weighted graphs, namely compact edge-coloring and circular compact edge-coloring. First, we discuss relations between these two coloring models. We prove that every outerplanar bipartite graph admits a compact edge-coloring and that the decision problem of the existence of compact circular edge-coloring is NP-complete in general. Then we provide a polynomial time 1:5-approximation algorithm and pseudo-polynomial exact algorithm for compact circular coloring of odd cycles and prove that it is NP-hard to optimally color these graphs. Finally, we prove that if a path P2 is joined by an edge to an odd cycle then the problem of the existence of a compact circular coloring becomes NP-complete.

scholarly journals Ramsey Numbers of Trees Versus Odd Cycles

10.37236/5731 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Matthew Brennan
Keyword(s):  
Positive Integer ◽  
Constant Factor ◽  
Linear Functions ◽  
Ramsey Numbers ◽  
Odd Cycle ◽  
Odd Cycles

Burr, Erdős, Faudree, Rousseau and Schelp initiated the study of Ramsey numbers of trees versus odd cycles, proving that $R(T_n, C_m) = 2n - 1$ for all odd $m \ge 3$ and $n \ge 756m^{10}$, where $T_n$ is a tree with $n$ vertices and $C_m$ is an odd cycle of length $m$. They proposed to study the minimum positive integer $n_0(m)$ such that this result holds for all $n \ge n_0(m)$, as a function of $m$. In this paper, we show that $n_0(m)$ is at most linear. In particular, we prove that $R(T_n, C_m) = 2n - 1$ for all odd $m \ge 3$ and $n \ge 25m$. Combining this with a result of Faudree, Lawrence, Parsons and Schelp yields $n_0(m)$ is bounded between two linear functions, thus identifying $n_0(m)$ up to a constant factor.

scholarly journals Vertex-Transitive Direct Products of Graphs

10.37236/6999 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Richard H. Hammack ◽  
Wilfried Imrich
Keyword(s):  
Direct Product ◽  
Direct Products ◽  
Odd Cycle ◽  
Vertex Transitive ◽  
Odd Cycles

It is known that for graphs $A$ and $B$ with odd cycles, the direct product $A\times B$ is vertex-transitive if and only if both $A$ and $B$ are vertex-transitive. But this is not necessarily true if one of $A$ or $B$ is bipartite, and until now there has been no characterization of such vertex-transitive direct products. We prove that if $A$ and $B$ are both bipartite, or both non-bipartite, then $A\times B$ is vertex-transitive if and only if both $A$ and $B$ are vertex-transitive. Also, if $A$ has an odd cycle and $B$ is bipartite, then $A\times B$ is vertex-transitive if and only if both $A\times K_2$ and $B$ are vertex-transitive.

scholarly journals On Decomposing Graphs of Large Minimum Degree into Locally Irregular Subgraphs

10.37236/5173 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Jakub Przybyło
Keyword(s):  
Connected Graph ◽  
Special Class ◽  
Maximum Degree ◽  
Minimum Degree ◽  
Probabilistic Approach ◽  
The Family ◽  
Edge Colourings ◽  
Odd Cycles

A locally irregular graph is a graph whose adjacent vertices have distinct degrees. We say that a graph G can be decomposed into k locally irregular subgraphs if its edge set may be partitioned into k subsets each of which induces a locally irregular subgraph in G. It has been conjectured that apart from the family of exceptions which admit no such decompositions, i.e., odd paths, odd cycles and a special class of graphs of maximum degree 3, every connected graph can be decomposed into 3 locally irregular subgraphs. Using a combination of a probabilistic approach and some known theorems on degree constrained subgraphs of a given graph, we prove this to hold for graphs of minimum degree at least $10^{10}$. This problem is strongly related to edge colourings distinguishing neighbours by the pallets of their incident colours and to the 1-2-3 Conjecture. In particular, the contribution of this paper constitutes a strengthening of a result of Addario-Berry, Aldred, Dalal and Reed [J. Combin. Theory Ser. B 94 (2005) 237-244].

Half-integral packing of odd cycles through prescribed vertices

COMBINATORICA ◽  
2013 ◽  
Vol 33 (5) ◽  
pp. 549-572 ◽  
Author(s):  
Naonori Kakimura ◽  
Ken-Ichi Kawarabayashi
Keyword(s):  
Odd Cycles

scholarly journals A decidable subclass of finitary programs

2010 ◽  
Vol 10 (4-6) ◽  
pp. 481-496 ◽  
Author(s):  
SABRINA BASELICE ◽  
PIERO A. BONATTI
Keyword(s):  
Problem Solving ◽  
Answer Set Programming ◽  
Stable Model ◽  
Unique Combination ◽  
Logic Programs ◽  
Trade Off ◽  
Full Support ◽  
Odd Cycles ◽  
Answer Set

AbstractAnswer set programming—the most popular problem solving paradigm based on logic programs—has been recently extended to support uninterpreted function symbols (Syrjänen 2001, Bonatti 2004; Simkus and Eiter 2007; Gebseret al. 2007; Baseliceet al. 2009; Calimeriet al. 2008). All of these approaches have some limitation. In this paper we propose a class of programs called FP2 that enjoys a different trade-off between expressiveness and complexity. FP2 is inspired by the extension of finitary normal programs with local variables introduced in (Bonatti 2004, Section 5). FP2 programs enjoy the following unique combination of properties: (i) the ability of expressing predicates with infinite extensions; (ii) full support for predicates with arbitrary arity; (iii) decidability of FP2 membership checking; (iv) decidability of skeptical and credulous stable model reasoning for call-safe queries. Odd cycles are supported by composing FP2 programs with argument restricted programs.

scholarly journals Maximum packings with odd cycles

1994 ◽  
Vol 131 (1-3) ◽  
pp. 91-97 ◽  
Author(s):  
Saad I. El-Zanati
Keyword(s):  
Odd Cycles ◽  
Maximum Packings
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