Results 81 to 90 of about 267 (133)

An introduction to the k-defect polynomials

, 2019
The 0-defect polynomial of a graph is just the chromatic polynomial. This polynomial has been widely studied in the literature. Yet little is known about the properties of k-defect polynomials of graphs in general, when 0 < k ≤ |E(G)|.
Mphako-Banda, Eunice
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Maximum Edge-Colorings Of Graphs

Discussiones Mathematicae Graph Theory, 2016
An r-maximum k-edge-coloring of G is a k-edge-coloring of G having a property that for every vertex v of degree dG(v) = d, d ≥ r, the maximum color, that is present at vertex v, occurs at v exactly r times. The r-maximum index χr′(G)$\chi _r^\prime (G)$
Jendrol’ Stanislav, Vrbjarová Michaela   +1 more
doaj   +1 more source

Further results on monotonic graph invariants and bipartiteness number

, 2019
The bipartiteness of a graph is the minimum number of vertices whose deletion from G results in a bipartite graph. If a graph invariant decreases or increases with addition of edges of its complement, then it is called a monotonic graph invariant.
Liu, Jia-Bao, Chen, Hanlin
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Facial Incidence Colorings of Embedded Multigraphs

Discussiones Mathematicae Graph Theory, 2019
Let G be a cellular embedding of a multigraph in a 2-manifold. Two distinct edges e1, e2 ∈ E(G) are facially adjacent if they are consecutive on a facial walk of a face f ∈ F(G). An incidence of the multigraph G is a pair (v, e), where v ∈ V (G), e ∈ E(G)
Jendrol’ Stanislav, Horňák Mirko, Soták Roman   +2 more
doaj   +1 more source

Edge-face total chromatic number of 3-regular Halin graphs, Congressus Numerantium

, 2000
A Halin graph is a plane graph H = T ∪ C, where T is a plane tree with no vertex of degree two and at least one vertex of degree three or more, and C is a cycle connecting the end vertices of T in the cyclic order determined by a plane embedment of T. In
Wai Chee Shiu, Bor Lam, Wai Hong Chan, Peter Che   +3 more
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Tr-Span of Directed Wheel Graphs

Discussiones Mathematicae Graph Theory, 2018
In this paper, we consider T-colorings of directed graphs. In particular, we consider as a T-set the set Tr = {0, 1, 2, . . ., r−1, r+1, . . .}. Exact values and bounds of the Tr-span of directed graphs whose underlying graph is a wheel graph are ...
Besson Marc, Tesman Barry
doaj   +1 more source

Largely Blocked C 4 -Designs Mathematics Subject Classification: 05B05; 05C15

, 2013
The problem to determine the existence of possible blocking sets ...
Mario Gionfriddo, Lorenzo Milazzo
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Game Chromatic Number of Graphs

, 1998
We show that if a graph has acyclic chromatic number k, then its game chromatic number is at most k(k + 1). By applying the known upper bounds for the acyclic chromatic numbers of various classes of graphs, we obtain upper bounds for the game chromatic ...
Xuding Zhu, Thomas Dinski
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Some Results on the Structure of Multipoles in the Study of Snarks ∗

, 2014
AMS classification: 05C15, 05C05, 05C38. Multipoles are the pieces we obtain by cutting some edges of a cubic graph. As a result of the cut, a multipole M has dangling edges with one free end, which we call semiedges.
J. Vilaltella, M. A. Fiol
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List Edge Colourings of Some 1-Factorable Multigraphs

, 1996
The List Edge Colouring Conjecture asserts that, given any multigraph G with chromatic index k and any set system fSe : e 2 E(G)g with each jSe j = k, we can choose elements se 2 Se such that se 6= sf whenever e and f are adjacent edges.
Luis Goddyn, M. N. Ellingham
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