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Odd Wheels in Graphs
2002
Journal of combinatorial theory. Series B (Print)
In this paper it is shown that if a graph G of order n with minimum degree greater than 7n/12 is at least 4-chromatic then G contains an odd wheel with at most 5 spokes. ...
For k \ 1 the odd wheel of 2k+1 spokes, denoted by W 2k+1 , is the graph obtained from a cycle of length 2k+1 by adding a new vertex and joining it to all vertices of the cycle. ...
ODD WHEELS IN GRAPHS ...
doi:10.1006/jctb.2001.2073
fatcat:z3dt7teohzhbvcp63ks43bd22e
On building 4-critical plane and projective plane multiwheels from odd wheels
[article]
2012
arXiv
pre-print
We build unbounded classes of plane and projective plane multiwheels that are 4-critical that are received summing odd wheels as edge sums modulo two. ...
to odd cycle. ...
Construction 7 Let us take odd in number (k = 2q + 1) odd wheels and one wheel w q . ...
arXiv:1202.4862v1
fatcat:24iipbchb5dkxnx62vd4lj4ux4
h-perfect plane triangulations
[article]
2015
arXiv
pre-print
Other minimally t-imperfect graphs are even Möbius ladders, and the circular graph C 2 10 ; see Figure 5 . Only odd wheels will be of relevance in this note. ...
The loose wheel is a loose odd wheel if C has odd length, and if at least three of the segments are odd as well. Obviously, odd wheels are loose odd wheels. ...
arXiv:1511.07990v1
fatcat:c6kvvn7b3zax7bsmnfs3h7slga
On t-perfect triangulations of the projective plane
[article]
2017
arXiv
pre-print
Evidently, every odd wheel is a loose odd wheel and every graph that contains an odd wheel as a subgraph also contains an odd wheel as an induced subgraph. ...
Introduction Perfect graphs received considerous attention in graph theory. ...
arXiv:1702.03175v2
fatcat:gut4bvrj7zfl7djcbckcjxe33m
Odd wheels are not odd-distance graphs
[article]
2020
arXiv
pre-print
An odd wheel graph is a graph formed by connecting a new vertex to all vertices of an odd cycle. ...
We answer a question of Rosenfeld and Le by showing that odd wheels cannot be drawn in the plane such that the lengths of the edges are odd integers. ...
[7] on embeddings of wheels. We also thank Dömötör Pálvölgyi and our anonymous reviewers for valuable suggestions and encouragement. ...
arXiv:2008.10305v1
fatcat:xhmtcj44cjcwzjtiqpwikx5o2e
Even and odd holes in cap-free graphs
1999
Journal of Graph Theory
It is an old problem in graph theory to test whether a graph contains a chordless cycle of length greater than three (hole) with a specific parity (even, odd). ...
If a graph is strongly even-signable or strongly odd-signable, then it is cap-free. In fact, strongly even-signable graphs are those cap-free graphs that are even-signable. ...
In an even wheel (H, x), we can arbitrarily label odd all edges having x as endnode. ...
doi:10.1002/(sici)1097-0118(199904)30:4<289::aid-jgt4>3.0.co;2-3
fatcat:uy6ifepm6rd3zddyj7ikddnztm
Even and odd holes in cap‐free graphs
1999
Journal of Graph Theory
It is an old problem in graph theory to test whether a graph contains a chordless cycle of length greater than three (hole) with a specific parity (even, odd). ...
If a graph is strongly even-signable or strongly odd-signable, then it is cap-free. In fact, strongly even-signable graphs are those cap-free graphs that are even-signable. ...
In an even wheel (H, x), we can arbitrarily label odd all edges having x as endnode. ...
doi:10.1002/(sici)1097-0118(199904)30:4<289::aid-jgt4>3.3.co;2-v
fatcat:pjdh637ojfbebk5vks2zdcxcza
Triangle-free graphs that are signable without even holes
2000
Journal of Graph Theory
We characterize triangle-free graphs for which there exists a subset of edges that intersects every chordless cycle in an odd number of edges (TF odd-signable graphs). ...
These graphs arise as building blocks of a decomposition theorem (for cap-free odd-signable graphs) obtained by the same authors. We give a polytime algorithm to test membership in this class. ...
ACKNOWLEGMENT Ajai Kapoor was supported in part by a grant from Gruppo Nazionale Delle Ricerche-CNR. ...
doi:10.1002/1097-0118(200007)34:3<204::aid-jgt2>3.0.co;2-p
fatcat:d5uh3m7ybzbybnje6o3k46fx2q
An alternative approach for the anti-magic labelling of a wheel graph and a pendant graph
2021
Journal of Science
For wheel graph, we removed the middle vertex of the wheel graph and created a path graph using the vertices in the outer cycle of the wheel graph. ...
Wheel graph is a graph that contains a cycle of length and for which every graph vertex in the cycle is connected to one other graph vertex known as the "hub". ...
Hence, the wheel graphs is anti-magic. Now consider the vertex summation of each edges in pendant graph, which is shown in Table 2 . ...
doi:10.4038/jsc.v12i2.35
fatcat:hl567d7rovfrtizbut2w6idtae
Francis Guthrie's approach to The Four Color Problem
[article]
2018
arXiv
pre-print
The odd wheel is the only type of 4-critical graph in which one vertex always gets a unique color. This supports Frederic Guthrie's approach to the Four Color Problem. ...
be an odd cycle, and G must be an odd wheel. v Figure 5 For every non-wheel 4-critical graph G and for every vertex v in G there must be another vertex u, independent of v, in G that can be given the ...
Figure 4 The vertex and the cycle above make out a wheel, and since the cycle is odd, we have an odd wheel, which is the simplest type of 4-critical graph-and also the only type of 4-critical graph in ...
arXiv:1804.04658v1
fatcat:n7farqkqqfbspnsrjuikop5xfi
Characteristics of Fuzzy Wheel Graph and Hamilton Graph with Fuzzy Rule
2019
Zenodo
In this paper, we consider the wheel graph and also the hamilton graph using if then rules fuzzy numbers. ...
B "Characteristics of Fuzzy Wheel Graph and Hamilton Graph with Fuzzy Rule" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue ...
In we consider the wheel graph and also the hamilton graph using fuzzy numbers. ...
doi:10.5281/zenodo.3589328
fatcat:x5wuc6o7gveajavx5iqqg6zgbq
Reducing quadrangulations of the sphere and the projective plane
[article]
2017
arXiv
pre-print
The operation is mainly used in the field of t-perfect graphs. ...
We further show that a non-bipartite quadrangulation of the projective plane can be transformed into an odd wheel by t-contractions and deletions of degree-2 vertices. ...
A p-wheel W p is a graph consisting of a cycle (w 1 , . . . , w p , w 1 ) and a vertex v adjacent to all vertices of the cycle. A wheel W p is an odd wheel, if p is odd. ...
arXiv:1606.07662v3
fatcat:z2onopk4xvhezloj2elbuflere
Triangulated neighborhoods in even-hole-free graphs
2007
Discrete Mathematics
This implies that in an even-hole-free graph, with n nodes and m edges, there are at most n + 2m maximal cliques. ...
It also yields an O(n 2 m) algorithm that generates all maximal cliques of an even-hole-free graph. In fact these results are obtained for a larger class of graphs that contains even-hole-free graphs. ...
odd-signable graph in time O(n 2 m). ...
doi:10.1016/j.disc.2006.07.027
fatcat:egwwswsnpbembk3ueum53tnvca
Some Results on 2-odd Labeling of Graphs
2020
International journal of recent technology and engineering
In this paper, we investigate 2-odd labeling of some classes of graphs. ...
A graph is said to be a 2-odd graph if the vertices of can be labelled with integers (necessarily distinct) such that for any two vertices which are adjacent, then the modulus difference of their labels ...
MAIN RESULTS In this section, we establish 2-odd labeling of some graphs such as wheel graph, fan graph, generalized butterfly graph, the line graph of sunlet graph, and shell graph. Lemma 1. ...
doi:10.35940/ijrte.e7041.018520
fatcat:o5vsskvugvblrpg7tjyhz26fte
On chordal and perfect plane near-triangulations
[article]
2019
arXiv
pre-print
or f induces an odd hole. ...
The above characterization leads to a linear time algorithm for determining perfectness of this class of graphs. ...
Definition 2.1 (Wheel). A wheel on n (n ≥ 4) vertices, W n , is the graph obtained by adding a new vertex v to C n−1 and making it adjacent to all vertices in C n−1 . ...
arXiv:1701.03447v3
fatcat:yncpnelhhjbf5pgpcgcf7gycqa
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