On <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.890499pt" id="M1" height="18.3634pt" version="1.1" viewBox="-0.0657574 -15.4729 141.734 18.3634" width="141.734pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g50-41" d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"/></g><g transform="matrix(.017,0,0,-0.017,6.143,0)"><path id="g50-108" d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z"/></g><g transform="matrix(.017,0,0,-0.017,14.878,0)"><path id="g50-45" d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"/></g><g transform="matrix(.017,0,0,-0.017,21.857,0)"><use xlink:href="#g50-108"/></g><g transform="matrix(.017,0,0,-0.017,30.814,0)"><path id="g50-111" d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"/></g><g transform="matrix(.017,0,0,-0.017,43.482,0)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g><g transform="matrix(.017,0,0,-0.017,57.848,0)"><use xlink:href="#g50-108"/></g><g transform="matrix(.012,0,0,-0.012,66.582,-7.751)"><path id="g50-51" d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"/></g><g transform="matrix(.017,0,0,-0.017,76.993,0)"><use xlink:href="#g54-33"/></g><g transform="matrix(.017,0,0,-0.017,91.359,0)"><use xlink:href="#g50-51"/></g><g transform="matrix(.017,0,0,-0.017,99.715,0)"><use xlink:href="#g50-108"/></g><g transform="matrix(.017,0,0,-0.017,112.332,0)"><use xlink:href="#g54-33"/></g><g transform="matrix(.017,0,0,-0.017,126.698,0)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g><g transform="matrix(.017,0,0,-0.017,135.054,0)"><path id="g50-42" d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z"/></g></svg>-Choosability of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2724395pt" id="M2" height="8.19251pt" version="1.1" viewBox="-0.0657574 -7.92007 8.95038 8.19251" width="8.95038pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><use xlink:href="#g50-111"/></g></svg>-Vertex Graphs

<div>The graph for Lemma <a href="https://static.hindawi.com/articles/ijmms/volume-2015/690517/figures/#lem2.7">10</a>.</div>

International Journal of Mathematics and Mathematical Sciences

fig1

Figure 1

Figure 1: On <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.890499pt" id="M1" height="18.3634pt" version="1.1" viewBox="-0.0657574 -15.4729 141.734 18.3634" width="141.734pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g50-41" d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"/></g><g transform="matrix(.017,0,0,-0.017,6.143,0)"><path id="g50-108" d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z"/></g><g transform="matrix(.017,0,0,-0.017,14.878,0)"><path id="g50-45" d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"/></g><g transform="matrix(.017,0,0,-0.017,21.857,0)"><use xlink:href="#g50-108"/></g><g transform="matrix(.017,0,0,-0.017,30.814,0)"><path id="g50-111" d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"/></g><g transform="matrix(.017,0,0,-0.017,43.482,0)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g><g transform="matrix(.017,0,0,-0.017,57.848,0)"><use xlink:href="#g50-108"/></g><g transform="matrix(.012,0,0,-0.012,66.582,-7.751)"><path id="g50-51" d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"/></g><g transform="matrix(.017,0,0,-0.017,76.993,0)"><use xlink:href="#g54-33"/></g><g transform="matrix(.017,0,0,-0.017,91.359,0)"><use xlink:href="#g50-51"/></g><g transform="matrix(.017,0,0,-0.017,99.715,0)"><use xlink:href="#g50-108"/></g><g transform="matrix(.017,0,0,-0.017,112.332,0)"><use xlink:href="#g54-33"/></g><g transform="matrix(.017,0,0,-0.017,126.698,0)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g><g transform="matrix(.017,0,0,-0.017,135.054,0)"><path id="g50-42" d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z"/></g></svg>-Choosability of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2724395pt" id="M2" height="8.19251pt" version="1.1" viewBox="-0.0657574 -7.92007 8.95038 8.19251" width="8.95038pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><use xlink:href="#g50-111"/></g></svg>-Vertex Graphs 

International Journal of Mathematics and Mathematical Sciences

On -Choosability of -Vertex Graphs

Figure 1