The graph of type (0, ∞, ∞) realizations of a graphic sequence

1979 ◽  
pp. 41-54 ◽  
Author(s):  
R. B. Eggleton ◽  
D. A. Holton
Keyword(s):  
Graphic Sequence

scholarly journals Transforming Graphs with the Same Graphic Sequence

2017 ◽  
Vol 25 (0) ◽  
pp. 627-633 ◽  
Author(s):  
Sergey Bereg ◽  
Hiro Ito
Keyword(s):  
Graphic Sequence

scholarly journals New Results on Degree Sequences of Uniform Hypergraphs

10.37236/3414 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
Sarah Behrens ◽  
Catherine Erbes ◽  
Michael Ferrara ◽  
Stephen G. Hartke ◽  
Benjamin Reiniger ◽  
...  
Keyword(s):  
Efficient Algorithm ◽  
Necessary Conditions ◽  
Degree Sequence ◽  
Sufficient Conditions ◽  
Degree Sequences ◽  
Uniform Hypergraph ◽  
Graphic Sequence ◽  
Uniform Hypergraphs ◽  
Open Question

A sequence of nonnegative integers is $k$-graphic if it is the degree sequence of a $k$-uniform hypergraph. The only known characterization of $k$-graphic sequences is due to Dewdney in 1975. As this characterization does not yield an efficient algorithm, it is a fundamental open question to determine a more practical characterization. While several necessary conditions appear in the literature, there are few conditions that imply a sequence is $k$-graphic. In light of this, we present sharp sufficient conditions for $k$-graphicality based on a sequence's length and degree sum.Kocay and Li gave a family of edge exchanges (an extension of 2-switches) that could be used to transform one realization of a 3-graphic sequence into any other realization. We extend their result to $k$-graphic sequences for all $k \geq 3$. Finally we give several applications of edge exchanges in hypergraphs, including generalizing a result of Busch et al. on packing graphic sequences.

scholarly journals HAMILTONICITY OF CAMOUFLAGE GRAPHS

2021 ◽  
Vol 5 (10) ◽  
Author(s):  
Sowmiya K
Keyword(s):  
Planar Graphs ◽  
Degree Sequence ◽  
Simple Graph ◽  
Hamilton Path ◽  
Graphic Sequence ◽  
Vertex Transitive ◽  
Connected Vertex

This paper examines the Hamiltonicity of graphs having some hidden behaviours of some other graphs in it. The well-known mathematician Barnette introduced the open conjecture which becomes a theorem by restricting our attention to the class of graphs which is 3-regular, 3- connected, bipartite, planar graphs having odd number of vertices in its partition be proved as a Hamiltonian. Consequently the result proved in this paper stated that “Every connected vertex-transitive simple graph has a Hamilton path” shows a significant improvement over the previous efforts by L.Babai and L.Lovasz who put forth this conjecture. And we characterize a graphic sequence which is forcibly Hamiltonian if every simple graph with degree sequence is Hamiltonian. Thus we discussed about the concealed graphs which are proven to be Hamiltonian.

scholarly journals An extremal problem for a graphic sequence to have a realization containing every 2-tree with prescribed size

2016 ◽  
Vol Vol. 17 no. 3 (Graph Theory) ◽  
Author(s):  
De-Yan Zeng ◽  
Jian-Hua Yin
Keyword(s):  
Lower Bound ◽  
Extremal Problem ◽  
Simple Graph ◽  
Graphic Sequence ◽  
International Audience

International audience A graph $G$ is a $2$<i>-tree</i> if $G=K_3$, or $G$ has a vertex $v$ of degree 2, whose neighbors are adjacent, and $G-v$ is a 2-tree. Clearly, if $G$ is a 2-tree on $n$ vertices, then $|E(G)|=2n-3$. A non-increasing sequence $\pi =(d_1, \ldots ,d_n)$ of nonnegative integers is a <i>graphic sequence</i> if it is realizable by a simple graph $G$ on $n$ vertices. Yin and Li (Acta Mathematica Sinica, English Series, 25(2009)795&#x2013;802) proved that if $k \geq 2$, $n \geq \frac{9}{2}k^2 + \frac{19}{2}k$ and $\pi =(d_1, \ldots ,d_n)$ is a graphic sequence with $\sum \limits_{i=1}^n d_i > (k-2)n$, then $\pi$ has a realization containing every tree on $k$ vertices as a subgraph. Moreover, the lower bound $(k-2)n$ is the best possible. This is a variation of a conjecture due to Erd&#x0151;s and S&oacute;s. In this paper, we investigate an analogue extremal problem for 2-trees and prove that if $k \geq 3$, $n \geq 2k^2-k$ and $\pi =(d_1, \ldots ,d_n)$ is a graphic sequence with $\sum \limits_{i=1}^n d_i > \frac{4kn}{3} - \frac{5n}{3}$ then $\pi$ has a realization containing every 2-tree on $k$ vertices as a subgraph. We also show that the lower bound $\frac{4kn}{3} - \frac{5n}{3}$ is almost the best possible.

The Erdös-Jacobson-Lehel conjecture on potentiallyP k-graphic sequence is true

1998 ◽  
Vol 41 (5) ◽  
pp. 510-520 ◽  
Author(s):  
Jiongsheng Li ◽  
Zixia Song ◽  
Rong Luo
Keyword(s):  
Graphic Sequence

PARTIAL RESULT ON HADWIGER'S CONJECTURE

2010 ◽  
Vol 02 (03) ◽  
pp. 413-423 ◽  
Author(s):  
ZI-XIA SONG
Keyword(s):  
Degree Sequence ◽  
Simple Graph ◽  
Partial Result ◽  
Degree Sequences ◽  
Induced Subgraph ◽  
Graphic Sequence ◽  
Hadwiger's Conjecture ◽  
Hadwiger’S Conjecture

Let D = (d1, d2, …, dn) be a graphic sequence with 0 ≤ d1 ≤ d2 ≤ ⋯ ≤ dn. Any simple graph G with D its degree sequence is called a realization of D. Let R[D] denote the set of all realizations of D. We say that D is H-free if no graph in R[D] contains H as an induced subgraph. In this paper, we prove that Hadwiger's Conjecture is true for graphs whose degree sequences are claw-free or [Formula: see text]-free.

scholarly journals On the simultaneous edge coloring of graphs

2014 ◽  
Vol 06 (04) ◽  
pp. 1450049
Author(s):  
Behrooz Bagheri Gh. ◽  
Behnaz Omoomi
Keyword(s):  
Bipartite Graph ◽  
Edge Coloring ◽  
Close Relation ◽  
Bipartite Graphs ◽  
Double Cover ◽  
Edge Colorings ◽  
Graphic Sequence

A μ-simultaneous edge coloring of graph G is a set of μ proper edge colorings of G with a same color set such that for each vertex, the sets of colors appearing on the edges incident to that vertex are the same in each coloring and no edge receives the same color in any two colorings. The μ-simultaneous edge coloring of bipartite graphs has a close relation with μ-way Latin trades. Mahdian et al. (2000) conjectured that every bridgeless bipartite graph is 2-simultaneous edge colorable. Luo et al. (2004) showed that every bipartite graphic sequence S with all its elements greater than one, has a realization that admits a 2-simultaneous edge coloring. In this paper, the μ-simultaneous edge coloring of graphs is studied. Moreover, the properties of the extremal counterexample to the above conjecture are investigated. Also, a relation between 2-simultaneous edge coloring of a graph and a cycle double cover with certain properties is shown and using this relation, some results about 2-simultaneous edge colorable graphs are obtained.

scholarly journals A Chinese Patient with Pusher Syndrome and Unilateral Spatial Neglect Syndrome

2014 ◽  
Vol 41 (4) ◽  
pp. 493-497 ◽  
Author(s):  
Xiao-Wei Chen ◽  
Cheng-He Lin ◽  
Hua Zheng ◽  
Zhen-Lan Lin
Keyword(s):  
Behavioral Therapy ◽  
Clinical Manifestations ◽  
Chinese Patient ◽  
Spatial Neglect ◽  
Behavioral Characteristics ◽  
Unilateral Spatial Neglect ◽  
Graphic Sequence ◽  
Thalamic Hemorrhage ◽  
Pusher Syndrome ◽  
Neglect Syndrome

Objective:To observe clinical manifestations, behavioral characteristics, and effects of rehabilitation on a patient with pusher syndrome and unilateral spatial neglect caused by right thalamic hemorrhage.Methods:Assessment of pusher syndrome was made by the Scale for Contraversive pushing (SCP), and unilateral spatial neglect syndrome was diagnosed using line cancellation, letter and star cancellation, line bisection tests and copy and continuation of graphic sequence test. Behavioral therapy, occupational therapy, reading training and traditional Chinese medicine methods were adopted for treatment of pusher syndrome and unilateral spatial neglect.Results:The patient showed typical pusher syndrome and unilateral spatial neglect symptoms. The pusher syndrome and unilateral spatial neglect symptoms were significantly improved following rehabilitation treatments.Conclusions:Pusher syndrome and unilateral spatial neglect syndrome occurred simultaneously after right thalamic hemorrhage. Early rehabilitation therapy can reduce the symptoms of pusher syndrome and unilateral spatial neglect syndrome and improve motor function.

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