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The independence number in graphs of maximum degree three

13 years 11 months ago

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We prove that a K4-free graph G of order n, size m and maximum degree at most three has an independent set of cardinality at least 1 7 (4n - m - - tr) where counts the number of c...

Jochen Harant, Michael A. Henning, Dieter Rautenba...

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Id	Views	Title	Status

1	177	The independence number in graphs of maximum degree three	claim
2	161	On the geodetic number and related metric sets in Cartesian product graphs	claim
3	145	Clique coverings and partitions of line graphs	claim
4	139	On domination and reinforcement numbers in trees	claim
5	137	Nordhaus-Gaddum results for restrained domination and total restrained domination in graphs	claim
6	129	On 3-regular 4-ordered graphs	claim
7	129	On association schemes all elements of which have valency 1 or 2	claim
8	127	On cyclically orientable graphs	claim
9	127	An adjacency lemma for critical multigraphs	claim
10	125	Difference systems of sets and cyclotomy	claim
11	123	Graphic sequences with a realization containing a generalized friendship graph	claim
12	119	A generalised upper bound for the k-tuple domination number	claim
13	117	Classes of optical orthogonal codes from arcs in root subspaces	claim
14	116	Total and fractional total colourings of circulant graphs	claim
15	116	Breaking the rhythm on graphs	claim
16	115	Characterizations of postman sets	claim
17	114	Subdivisions of graphs: A generalization of paths and cycles	claim
18	113	On some colouring of 4-cycle systems with specified block colour patterns	claim
19	113	Multivariate Fuss-Catalan numbers	claim
20	112	Orbit-counting polynomials for graphs and codes	claim
21	112	Coloring the Cartesian sum of graphs	claim
22	112	On the vertices of the k-additive core	claim
23	111	Planarity of iterated line graphs	claim
24	110	A novel algorithm enumerating bent functions	claim
25	110	Nonrepetitive colorings of graphs of bounded tree-width	claim
26	110	Contractible subgraphs, Thomassen's conjecture and the dominating cycle conjecture for snarks	claim
27	107	Set maps, umbral calculus, and the chromatic polynomial	claim
28	106	Chromatic capacity and graph operations	claim
29	105	Fibonacci numbers, alternating parity sequences and faces of the tridiagonal Birkhoff polytope	claim
30	104	On edge-weighted recursive trees and inversions in random permutations	claim
31	104	Improved upper and lower bounds on the feedback vertex numbers of grids and butterflies	claim
32	103	Improper colouring of (random) unit disk graphs	claim
33	103	A note on lattice chains and Delannoy numbers	claim
34	103	Edge-colorings avoiding rainbow and monochromatic subgraphs	claim
35	102	Largest subsemigroups of the full transformation monoid	claim
36	101	Congruences involving Bernoulli polynomials	claim
37	100	Cyclic sequences of k-subsets with distinct consecutive unions	claim
38	100	Adaptive group testing for consecutive positives	claim
39	100	Staircase tilings and k-Catalan structures	claim
40	100	Constructing and classifying neighborhood anti-Sperner graphs	claim
41	100	Variations of Y-dominating functions on graphs	claim
42	98	Constructing equidissections for certain classes of trapezoids	claim
43	97	(r, r+1)-factorizations of (d, d+1)-graphs	claim
44	97	On uniquely k-determined permutations	claim
45	97	On the integral ring spanned by genus two weight enumerators	claim
46	97	On extremal k-outconnected graphs	claim
47	96	Generating 3-vertex connected spanning subgraphs	claim
48	95	General neighbour-distinguishing index of a graph	claim
49	95	Forbidden subgraphs and the existence of paths and cycles passing through specified vertices	claim
50	94	On low degree k-ordered graphs	claim
51	94	Discrete transformation hypergroups and transformation hypergroups with phase tolerance space	claim
52	93	Nonbinary quantum error-correcting codes from algebraic curves	claim
53	93	The s-Hamiltonian index	claim
54	92	Partial cubes: structures, characterizations, and constructions	claim
55	91	Further results on large sets of Kirkman triple systems	claim
56	91	Lower bounds for the game colouring number of partial k-trees and planar graphs	claim
57	91	An isoperimetric inequality in the universal cover of the punctured plane	claim
58	90	Retractions onto series-parallel posets	claim
59	90	On sums of binomial coefficients and their applications	claim
60	89	Primitive 2-factorizations of the complete graph	claim
61	89	Combinatorics of sequential dynamical systems	claim
62	89	Nearlattices	claim
63	88	Packing triangles in low degree graphs and indifference graphs	claim
64	88	Bijective proofs of Gould's and Rothe's identities	claim
65	88	Degree sequence and supereulerian graphs	claim
66	88	A technique to study the correlation measures of binary sequences	claim
67	88	Lower bounding the boundary of a graph in terms of its maximum or minimum degree	claim
68	87	More on pooling spaces	claim
69	86	"Catalan traffic" and integrals on the Grassmannian of lines	claim
70	86	Hamiltonian properties of triangular grid graphs	claim
71	85	All graphs with maximum degree three whose complements have 4-cycle decompositions	claim
72	84	Cyclic hamiltonian cycle systems of the complete graph minus a 1-factor	claim
73	84	Multicoloring and Mycielski construction	claim
74	84	On diameter perfect constant-weight ternary codes	claim
75	83	Degree conditions on claws and modified claws for hamiltonicity of graphs	claim
76	83	The polynomial degrees of Grassmann and Segre varieties over GF(2)	claim
77	83	Diameter-girth sufficient conditions for optimal extraconnectivity in graphs	claim
78	83	Highly connected multicoloured subgraphs of multicoloured graphs	claim
79	82	2-Binary trees: Bijections and related issues	claim
80	82	Problems and results in extremal combinatorics - II	claim
81	82	Product action	claim
82	82	The distribution of the domination number of class cover catch digraphs for non-uniform one-dimensional data	claim
83	81	The diameter of protean graphs	claim
84	80	Restrained bondage in graphs	claim
85	80	On affine designs and Hadamard designs with line spreads	claim
86	79	Combinatorial properties of a general domination problem with parity constraints	claim
87	79	The reconstruction conjecture and edge ideals	claim
88	79	Chromatic coloring with a maximum color class	claim
89	78	On the minimum number of completely 3-scrambling permutations	claim
90	78	Planarization and fragmentability of some classes of graphs	claim
91	78	A symbolic operator approach to several summation formulas for power series II	claim
92	77	Degree sum and connectivity conditions for dominating cycles	claim
93	77	Distinguishing colorings of Cartesian products of complete graphs	claim
94	77	On 2-factors with k components	claim
95	77	Perfect Skolem sets	claim
96	76	Graphic sequences with a realization containing a complete multipartite subgraph	claim
97	76	On s-hamiltonian-connected line graphs	claim
98	75	Constructing strength three covering arrays with augmented annealing	claim
99	75	Contractibility and the clique graph operator	claim
100	75	Homogeneous factorisations of graph products	claim
101	75	A new characterization of HH-free graphs	claim
102	74	A degree sum condition for long cycles passing through a linear forest	claim
103	73	Graphs with the n-e.c. adjacency property constructed from affine planes	claim
104	73	Near automorphisms of cycles	claim
105	73	Connectivity in frame matroids	claim
106	73	A note on edge-graceful spectra of the square of paths	claim
107	73	On multipartite posets	claim
108	72	(p, 1)-Total labelling of graphs	claim
109	72	Equivariant collapses and the homotopy type of iterated clique graphs	claim
110	72	Paired bondage in trees	claim
111	70	Embedding balanced P3-designs into (balanced) P4-designs	claim
112	70	Enumeration of (k, 2)-noncrossing partitions	claim
113	70	A special class of tensor categories initiated by inverse braid monoids	claim
114	70	On the number of minimal transversals in 3-uniform hypergraphs	claim
115	69	Connectedness of the graph of vertex-colourings	claim
116	69	The signed-graphic representations of wheels and whirls	claim
117	69	New identities for 7-cores with prescribed BG-rank	claim
118	68	Heavy cycles in k-connected weighted graphs with large weighted degree sums	claim
119	68	Riordan paths and derangements	claim
120	68	Path bundles on n-cubes	claim
121	68	On embedding well-separable graphs	claim
122	67	Size of monochromatic components in local edge colorings	claim
123	66	Constructions of non-principal families in extremal hypergraph theory	claim
124	66	The Monochromatic Column problem	claim
125	65	On the L(p, 1)-labelling of graphs	claim
126	65	Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas	claim
127	65	Gaps in semigroups	claim
128	64	A combinatorial approach to doubly transitive permutation groups	claim
129	63	Nomadic decompositions of bidirected complete graphs	claim
130	63	Clifford theory for commutative association schemes	claim
131	63	Edge-connectivity augmentation of graphs over symmetric parity families	claim
132	63	Uniqueness of Walkup's 9-vertex 3-dimensional Klein bottle	claim
133	63	All triples for orthogonal designs of order 40	claim
134	62	Classification of some strongly regular subgraphs of the McLaughlin graph	claim
135	61	Neighborhood unions and extremal spanning trees	claim
136	61	Wilf classification of three and four letter signed patterns	claim
137	61	Inheritance of hyper-duality in imprimitive Bose-Mesner algebras	claim
138	61	Unbordered factors and Lyndon words	claim
139	60	Local topology of the free complex of a two-dimensional generalized convex shelling	claim
140	59	Matroid matching with Dilworth truncation	claim
141	59	On friendly index sets of 2-regular graphs	claim
142	59	On non-antipodal binary completely regular codes	claim
143	58	Newman's phenomenon for generalized Thue-Morse sequences	claim
144	58	A two-parameter family of an extension of Beatty sequences	claim
145	58	Incompleteness of the Giulietti-Ughi arc for large primes	claim
146	58	The determinants of certain matrices arising from the Boolean lattice	claim
147	58	The vertex isoperimetric problem for the powers of the diamond graph	claim
148	57	Packing non-returning A-paths algorithmically	claim
149	56	The game of arboricity	claim
150	56	Point-weight designs with design conditions on t points	claim
151	56	Note on the 3-graph counting lemma	claim
152	55	Rank functions of strict cg-matroids	claim
153	55	Improved pebbling bounds	claim
154	54	Strong edge-magic graphs of maximum size	claim
155	53	Distance graphs with maximum chromatic number	claim
156	53	Where the monotone pattern (mostly) rules	claim
157	52	On the pebbling threshold of paths and the pebbling threshold spectrum	claim
158	51	On embeddings of snarks in the torus	claim
159	51	Non-cover generalized Mycielski, Kneser, and Schrijver graphs	claim
160	51	Line-graphs of cubic graphs are normal	claim
161	50	On tree congestion of graphs	claim
162	50	Searching monotone multi-dimensional arrays	claim
163	49	Linear choosability of graphs	claim
164	49	Periodical states and marching groups in a closed owari	claim
165	48	Relative length of longest paths and longest cycles in triangle-free graphs	claim
166	48	A note on degree-constrained subgraphs	claim
167	47	Radio number for trees	claim
168	47	New constructions of two slim dense near hexagons	claim
169	46	Steiner centers and Steiner medians of graphs	claim
170	43	Subdivided trees are integral sum graphs	claim
171	33	The wheels of the OLS polytope: Facets and separation	claim

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