Results 41 to 50 of about 1,320 (180)
Journal of Graph Theory, EarlyView.ABSTRACT In an effort to understand the complexity of the maximum independent set problem, Chvátal introduced t‐perfect graphs. While a full characterization of this class remains open, important progress has been made for claw‐free graphs [Bruhn and Stein, Math. Program. 2012] and P 5 ${P}_{5}$‐free graphs [Bruhn and Fuchs, SIAM J. Discrete Math. 2017]
Yixin Cao, Shenghua Wang
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Explicit 3‐colorings for Exponential Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In 1985, El‐Zahar and Sauer showed that the chromatic number of the direct product of two 4‐chromatic graphs is 4, establishing a nontrivial case of Hedetniemi's conjecture, which has since been refuted in general. Their proof uses the concept of an exponential graph, showing that if a graph H $H$ has no proper 3‐coloring, then the exponential
Adrien Argento +2 more
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Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts
Advances in Fuzzy Systems, 2019 Coloring of fuzzy graphs has many real life applications in combinatorial optimization problems like traffic light system, exam scheduling, register allocation, etc.
Mamo Abebe Ashebo +1 more
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Path Degeneracy and Applications
Journal of Graph Theory, EarlyView.ABSTRACT In this work, we relate girth and path‐degeneracy in classes with sub‐exponential expansion, with explicit bounds for classes with polynomial expansion and proper minor‐closed classes that are tight up to a constant factor (and tight up to second order terms if a classical conjecture on existence of g $g$‐cages is verified). As an application,
Yuquan Lin, Patrice Ossona de Mendez
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On the chromatic number of (P_{5},windmill)-free graphs [PDF]
Opuscula Mathematica, 2017 In this paper we study the chromatic number of \((P_5, windmill)\)-free graphs. For integers \(r,p\geq 2\) the windmill graph \(W_{r+1}^p=K_1 \vee pK_r\) is the graph obtained by joining a single vertex (the center) to the vertices of \(p\) disjoint ...
Ingo Schiermeyer
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Expansions of the chromatic polynomial
Discrete Mathematics, 1973 AbstractThe chromatic polynomial (or chromial) of a graph was first defined by Birkhoff in 1912, and gives the number of ways of properly colouring the vertices of the graph with any number of colours. A good survey of the basic facts about these polynomials may be found in the article by Read [3].It has recently been noticed that some classical ...
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Properties of chromatic polynomials of hypergraphs not held for chromatic polynomials of graphs
European Journal of Combinatorics, 2017 3 figures, 22 pages, 48 references.
Ruixue Zhang, Fengming Dong
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Laser &Photonics Reviews, EarlyView.A dual‐layer metasurface is integrated on a fiber‐array facet to realize compact, plug‐and‐play free‐space optical links with cylindrical vector beam (CVB) space‐division multiplexing. An optimized off‐axis collimation layer steers multiple channels, while a Dammann vortex layer performs polarization–topology conversion for bidirectional CVB (de ...
Xipeng Lu +6 more
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Improved inclusion-exclusion identities via closure operators [PDF]
Discrete Mathematics & Theoretical Computer Science, 2000 Let (A v) v ∈ V be a finite family of sets. We establish an improved inclusion-exclusion identity for each closure operator on the power set of V having the unique base property.
Klaus Dohmen
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An inequality for chromatic polynomials
Discrete Mathematics, 1992 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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